modern physics

§ BANSALCLASSES TARGET IIT JEE 2007

XII (ALL)

QUESMOa MMEJM MODERN PHYSICS

QUESTION FOR SHORT ANSWER

ATOMIC PHYSICS

Q.l In the photoelectric effect, why does the existence of a cutoff frequency speak in favour of the photon theory and against the wave theory?

Q. 2 Explain the statement that one's eyes could not detect faint starlight if light were not particle-like.

Q. 3 How can a photon energy be given by E = h/when the very presence of the frequency/in the formula implies that light is a wave?

Q. 4 The momentum p of a photon is given by p = hIX. Why is it that c, the speed oflight, does not appear in this expression?

Q. 5 Given that E = h/'for a photon, the Doppler shift in frequency of radiation from a receding light source would seem to indicate a reduced energy for the emitted photons. Is this in fact true? If so, what happened to the conservation of energy principle?

Q. 6 Any series of atomic hydrogen yet to be observed will probably be found in what region of the spectrum? Q.7 Can a hydrogen atom absorb a photon whose energy exceeds its binding energy( 13.6 eV)?

Q. 8 Only a relatively small number of Balmer lines can be observed from laboratory discharge tubes, whereas a large number are observed in stellar spectra. Explain this in terms ofthe small density, high temperature, and large volume of gases in stellar atmospheres.

Q. 9 Wnat is the origin of the cutoff wavelength Xm m of figure shown? Why is it an important clue to the photon nature of x rays?

e u a <u >

30 40 50 60 70 80 90 Wavelength (pm)

Q. 10 Can atomic hydrogen be caused to emit x rays? If so, describe how. Ifnot, why not?

Q.l l Why is it that B ohr theory, which does not work very well even for helium (Z = 2), gives such a good account of the characteristic x-ray spectra of the elements, or at least of that portion that originates deep within the atom?

Q.12 The ionization potential of hydrogen is 13.6 V. Yet to obtain discharge in a cathode ray tube filled with hydrogen, a very high voltage ( ~104V) has to be applied across the tube. Explain this clearly. Also explain why the gas must be at low pressure to obtain discharge.

(fe Bansal Classes Question Bank on Modern Physics 12]

Q.13 X-rays are produced when a fast electron hits a proper target. What happens to the electron? Q.14 Why does the tail of a comet always point away from the sun?

Q.15 A neutron pion at rest decays into two gamma photons. 7t° —-> y + y

Why cannot a single photon be born? What conservation law is in contradiction with it?

Q.16 What is so special about e/m rather than e end m separately?

Q.17 Why is it advisable to view a TV screen from a distance of about ten feet? Q. 18 The electrical conductivity of a gas increases when X-rays or y-rays pass through it. Explain this

phenomenon. Q.19 In photoelectric emission exchange of energy takes place among... (photon and electron/' photon, electron

and lattice).

Q.20 The threshold frequencies for photoemission for three metals numbered 1,2,3 are respectively v p v v 3

and Vj > v 2 > v 3. An incident radiation of frequency v 0 > v 2 . . . cause photoemission from 3 but... cause photoemission from 1 (fill in the gaps with may, may not / will certainly).

NUCLEAR PHYSICS

Q. 1 Why does the relative importance of the Coulomb force compared to the strong nuclear force increase at large mass numbers?

Q.2 In your body, are there more neutrons than protons? More protons than electrons? Discuss

Q. 3 Why is the binding energy per nucleon (see figure) low at low mass numbers? At high mass numbers? Region of greatest r-^stability

Jnisiqp Fission —ii.. ~5 Br 120* f i V i j

!2H .. i — ' 1

0 20 40 60 80 100 120 MO 161) 180 200 220 240 Mass number, A

Q.4 Aradioactive nucleus can emit a positron, e+. This corresponds to a proton in the nucleus being converted to a neutron The mass of a neutron, however, is greater than that of a proton. How thai can positron emission occur?

Q.5 In beta decay the emitted electrons form a continuous spectrum, but in alpha decay the alpha particles form a discrete spectrum. What difficulties did this cause in the explanation of beta decay, and how were these difficulties finally overcome?


Q.6 How do neutrinos differ from photons? Each has zero charge and (presumably) zero rest mass and travels at the speed oflight.

Q.7 In radioactive dating with 2 3 8 U, how do you get around the fact that you do not know how much 2 3 8 U was present in the rocks to begin with? (Hint: What is the ultimate decay product of 2 3 8U?)

Q.8 If it is so much harder to get a nucleon out of a nucleus than to get an electron out of an atom, why try? Q.9 In the generalized equation for the fission of 2 3 5 U by thermal neutrons, 2 3 5 U + n -> X + Y + bn, do you

expect the Q of the reaction to depend on the identity of X and Y? Q.10 The half-life of 2 3 5 U is 7.0 x 108y. Discuss the assertion that ifit had turned out to be shorter by a factor

of 10 or so, there would not be any atomic bombs today. Q.ll The binding energy curve of figure tells us that any nucleus more massive than A « 5 6 can release energy

by the fission process. Only very massive nuclides seem to do so, however. Why cannot lead, for example, release energy by the fission process?

Region of greatest ^"stability

J - ' u s i q p Fiss ion

" ' " J r 5 Bp B r I20g

2 3 9 P u

7 4 H e 1 I 5 7 f l c ' ^ A u

• H . . i i — i——i——i——i—

0 20 40 60 80 1 00 120 140 160 180 200 220 240 Mass number, A Q.12 Elements up to mass number w 5 6 are created by thermonuclear fusion in the cores of stars. Why are

heavier elements not also created by this process? Q.13 Which would generate more radioactive waste products: - a fission reactor or a fusion reactor? Q. 14 How can Becquerel rays, i.e., the combination of a-, P- and y-rays, be separated? Q.15 When a nucleus undergoes a-decay, is the product atom electrically neutral? In (3-decay? Q.16 Experimental results in radioactivity show small variations from the results predicted by theory. Explain

this. Q.17 If a nucleus emits only a y-rays photon, does its mass number change? Does its mass change?


ONLY ONE OPTION IS CORRECT. Take approx. 2 minutes for answering each question.

Q. 1 Let n r and n b be respectively the number of photons emitted by a red bulb and a blue bulb of equal power in a given time.

£ (A)n r = n b ( B ) n r < n b ( C ) n r > n b (D) data insufficient Q.2 10~3 W of 5000 A light is directed on a photoelectric cell. If the current in the cell is 0.16 pA, the

percentage of incident photons which produce photoelectrons, is (A) 0.4% (B) .04% (C) 20% (D) 10% £

Q.3 A proton and an electron are accelerated by same potential difference have de-Broglie wavelength Xp and A,e. (A) Xe = Xp (B) < (C) Xe > Xp (D) none of these.

Q ,4 Two electrons are moving with the same speed v. One electron enters a region of uniform electric field while the other enters a region of uniform magnetic field, then after sometime ifthe de-Broglie wavelengths of the two are X{ and X2, then: (A) = X2 (B)Aj > X2 (C) Xl < X2 (D) X1 > X2 or Xl < X2

Q.5 In a photo-emissive cell, with exciting wavelength X, the maximum kinetic energy of electron is K. If the 3X exciting wavelength is changed to — the kinetic energy of the fastest emitted electron will be:

£

(A) 3K/4 (B) 4K/3 (C) less than 4K/3 (D) greater than 4K/3 Q.6 If the frequency of light in a photoelectric experiment is doubled, the stopping potential will

(A) be doubled (B) halved (C) become more than doubled (D) become less than double

Q.7 An electron with initial kinetic energy of 100 eV is acceleration through a potential difference of 5 0 V Now the de-Broglie wavelength of electron becomes

^ ( A ) l A ( B ) V L 5 A (C) V3 A (D) 12.27 A

Q.8 If h is Planck's constant is SI system, the momentum of a photon of wavelength 0.01 A is: (A) 10"2 h (B)h (C)10 2 h ^ (D) 10 1 2 h

Q. 9 The stopping potential for the photo electrons emitted from a metal surface of work function 1.7 eV is 10.4 V. Identify the energy levels corresponding to the transitions in hydrogen atom which will result in emission of wavelength equal to that of incident radiation for the above photoelectric effect (A)n = 3 to 1 (B)n = 3 to 2 ( C ) n = 2 t o l (D)n = 4 t o l

Q.10 When a photon of light collides with a metal surface, number of electrons, (if any) coming out is (A) only one (B) only two (C) infinite (D) depends upon factors

£ Q. 11 Two radioactive material Aj and ^ have decay constants of 10 X0 and X0. If initially they have same

number of nuclei, the ratio of number of their undecayed nuclei will be (1/e) after a time L 1 1 ( A ) r ^ ^ ( c> i s : 1

dl Bansal Classes Question Bank on Modern Physics i

[5]

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Q.12 The frequency and the intensity of a beam oflight falling on the surface of photoelectric material are increased by a factor of two. This will: (A) increase the maximum energy of the photoelectrons, as well as photoelectric current by a factor of two. (B) increase the maximum kinetic energy of the photo electrons and would increase the photoelectric current by a factor of two. (C) increase the maximum kinetic energy of the photoelectrons by a factor of greater than two and will have no effect on the magnitude of photoelectric current produced. (D) not produce any effect on the kinetic energy of the emitted electrons but will increase the photoelectric current by a factor of two.

Q J o Light coming from a discharge tube filled with hydrogen falls on the cathode of the photoelectric cell. The work function of the surface of cathode is 4eV Which one of the following values of the anode voltage (in Volts) with respect to the cathode will likely to make the photo current zero. (A) - 4 ( B ) - 6 (C) - 8 ( D ) - 1 0

Q. 14 A point source of ligth is used in a photoelectric effect. If the source is removed farther from the emitting metal, the stopping potential: (A) will increase (B) will decrease (C) will remain constant (D) will either increase or decrease.

QJ/5 A point source causes photoelectric effect from a small metal plate. Which of the following curves may represent the saturation photocurrent as a function of the distance between the source and the metal ?

(A) (B) (C) (D) Q.16 Let Kj be the maximum kinetic energy of photoelectrons emitted by a light of wavelength A, and K 2

corresponding to X2. If = 2"k2, then: (A) 2Kj = K 2 (B) K, - 2K 2 ( C ) K , < | (D) K, > 2K 2

Q. 17 In a photoelectric experiment, the potential difference V that must be maintained between the illuminated surface and the collector so as just to prevent any electron from reaching the collector is determined for different frequencies f of the incident illumination. The graph obtained is shown. The maximum kinetic energy of the electrons emitted at frequency f, is

Vi ( B ) 7fT3i (A) iff. ( C ) h ( f 1 - f 0 ) ( D ) e V 1 ( f 1 - f 0 ) M v ^ ( f i - f o )

Q.18 Radiation oftwo photon energies twice and five times the work function of metal are incident sucessively on the metal surface. The ratio of the maximum velocity of photoelectrons emitted is the two cases will be (A) 1 :2 (B)2 . 1 (C) 1 4 (D)4: 1

Q.19 Cut off potentials for a metal in photoelectric effect for light of wavelength X x,X 2 and X3 is found to be Vj, V 2 and V 3 volts if Vj, V 2 and V 3 are inArithmetic Progression and A,,, X2 and A3 will be: (A) Arithmetic Progression (B) Geometric Progression (C) Harmonic Progression (D) None


Q. 20 Photons with energy 5 eV are incident on a cathode C, on a photoelectric cell. The maximum energy of the emitted photoelectrons is 2 eV. When photons of energy 6 eV are incident on C, no photoelectrons

C will reach the anode A if the stopping potential of A relative to C is (A)3 V (B) -3V ( C ) - 1 V (D)4 V

Q.21 In a photoelectric experiment, the collector plate is at 2.0V with respect to the emitter plate made of copper cp - 4.5eV). The emitter is illuminated by a source of monochromatic light ofwavelength 200nm. (A) the minimum kinetic energy ofthe photoelectrons reaching the collector is 0. (B) the maximum kinetic energy of the photoelectrons reaching the collector is 3,7eV.

p (C) if the polarity of the battery is reversed then answer to part A will be 0. (D) if the polarity of the battery is reversed then answer to part B will be 1,7eV.

Q.22 By increasing the intensity of incident light keeping frequency (v > v 0 ) fixed on the surface of metal (A) kinetic energy of the photoelectrons increases (B) number of emitted electrons increases (C) kinetic energy and number of electrons increases (D) no effect

Q.23 In a photoelectric experiment, electrons are ejected from metals X and Y by light of intensity I and frequency f. The potential difference V required to stop the electrons is measured for various frequencies. If Y has a greater work function than X; which one of the following graphs best illustrates the expected results?

V Vi X / / < (B)

f o

V X

(C) 0

V

4 (D) •f o

Y /

Q. 2,4 Monochromatic light with a frequency well above the cutoff frequency is incident on the emitter in a photoelectric effect apparatus. The frequency of the light is then doubled while the intensity is kept constant. How does this affect the photoelectric current? (A) The photoelectric current will increase. (B) The photoelectric current will decrease. (C),The photoelectric current will remain the same. (D) None of these

Q. 2 5 In a hypothetical system a particle of mass m and charge - 3 q is moving around a very heavy particle having cahrge q. Assuming Bohr's model to be true to this system, the orbital velocity of mass m when it is nearest to heavy particle is

3q 2 3q 2 3q 3q

Q. 26 de-Broglie wavelength of an electron in the nth B ohr orbit is \ and the angular momentum is Jn, then:

" (A) J n x (B) ln oc 7~ (C) Xn cc j 2 (D) none of these ** rt

q s * cvr\i f

$$ Bansal Classes Question Bank on Modern Physics m

Q.27 The angular momentum of an electron in the hydrogen atom is — . Here h is Planck's constant. The \ 2tc kinetic energy of this electron is: (A)4.53 eV (B)1.51eV (C)3.4eV (D)6.8eV

Q.28 Consider the following electronic energy level diagram of H-atom: Photons associated with shortest and longest wavelengths would be emitted from the atom by the transitions labelled: (A) D and C respectively (B) C and A respectively

A D C

B

- n = oo

- n = 4

- n = 3

- n = 2

(C) C and D respectively n = j (D) Aand C respectively

Q.29 In a hydrogen atom, the binding energy of the electron in the n t h state is E n , then the frquency of revolutionof the electron in the nth orbits is: (A)2E n/nh . (B) 2Enn/h (C)E n/nh (D)E nn/h

Q.30 Ifthe electron in a hydrogen atom were in the energy level with n=3, how much energy in joule would be required to ionise the atom? (Ionisation energy of H-atomis 2.18 x 10""18J): (A) 6.54 x 10" 1 9 (B) 1.43 x 10" 1 9 (C) 2.42 x 10~19 (D) 3.14 x 10" 2 0

Q.31 In hydrogen and hydrogen like atoms, the ratio of difference of energies E 4 n - E 2 n and E 2 n - E n varies with its atomic number z and n as: (A)z 2 /n 2 (B) zVn4 (C)z /n (D)z°n°

Q.32 In a hydrogen atom, the electron is in nth excited state. It may come down to second excited state by . emitting ten different wavelengths. What is the value of n:

(A) 6 (B) 7 (C) 8 (D) 5

Q.33 Difference between nth and (n+1 )th Bohr's radius of 'H' atom is equal to it's (n-1 )th Bohr's radius, the value ofnis: (A) 1 (B) 2 (C) 3 (D) 4

Q.34 An electron in hydrogen atom after absorbing energy photons can jump between energy states n t and n2(n, > nj). Then it may return to ground state after emitting six different wavelengths in emission spectrum.

| the energy of emitted photons is either equal to, less than or greater than the absorbed photons. Then nj and n 2 are: (A) n 2 = 4, n } = 3 (B)n 2 = 5 ,n j=3 (C)n 2 = 4, n, = 2 (D) n 2 = 4 , ^ = 1

Q.35 The electron in a hydrogen atom makes transition from M shell to L. The ratio of magnitudes of initial to final centripetal acceleration of the electron is (A) 9 : 4 (B)81:16 ( C ) 4 : 9 (D)16:81

Q.36 The electron in a hydrogen atom makes a transition n, —> n 2 whose nj and n 2 are the principal quantum numbers of the two states. Assume the Bohr model to be valid. The frequency of orbital motion of the electron in the initial state is 1/27 of that in the final state. The possible values of n t and n 2 are (A) n t =4, n 2 = 2 ( 6 ) ^ = 3 , ^ = 1 ( 0 ) ^ = 8 , ^ = 1 ( 0 ) ^ = 6 , ^ = 3

Q.37 The radiu s of B ohr' s first orbit is a 0. The electron in n t h orbit has a radiu s: (A) na 0 (B)a 0/n (C)n 2 a 0 (D)a 0 /n 2


Q.38 The ionisation potential of hydrogen atom is 13.6 volt. The energy required to remove an electron from ^ the second orbit of hydrogen is:

(A) 3.4 eV (B)6.8eV (C)13.6eV (D)27.2eV Q.39 Electron in a hydrogen atom is replaced by an identically charged particle muon with mass 207 times that

of electron. Now the radius of K shell will be (A) 2.56 x 10~3 A (B) 109.7 A (C) 1.21 x 10~3 A (D)22174.4A

Q.40 Monochromatic radiation of wavelength X is incident on ahydrogen sample containing in ground state. Hydrogen atoms absorb the light and subsequently emit radiations of ten different wavelengths. The -value of X is (A) 95 nm (B)103nm (C)73nm (D)88nm

Q.41 When a hydrogen atom, initially at rest emits, a photon resulting in transition n = 5 -> n = 1, its recoil speed is about (A) 10^ m/s (B) 2 x 10"2 m/s (C) 4.2 m/s (D) 3.8 x l(T 2 m/s

Q. 42 An electron collides with a fixed hydrogen atom in its ground state. Hydrogen atom gets excited and the colliding electron loses all its kinetic energy. Consequently the hydrogen atom may emit a photon corresponding to the largest wavelength of the Balmer series. The min. K.E. of colliding electron will be (A) 10.2 eV (B) 1.9 eV (C)12.1eV (D)13.6eV

Q.43 The frequency of revolution of electron in n t h Bohr orbit is v n . The graph between log n and log (v n / v,) may be

Q. 44 Consider the spectral line resulting from the transition n = 2 —» n = 1 in the atoms and ions given below. The shortest wavelength is produced by: (A) hydrogen atom (B) deuterium atom (C) singly ionized helium (D) doubly ionized lithium

Q.45 In an atom, two electrons move around the nucleus in circular orbits of radii R and 4R. The ratio of the time taken by them to complete one revolution is: (neglect electric interaction) (A) 1 :4 (B) 4 : 1 (C) 1 : 8 (D) 8 : 1

Q.46 The electron in hydrogen atom in a sample is in n l h excited state, then the number of different spectrum lines obtained in its emission spectrum will be: (A) 1 + 2 + 3 + +(n - 1) (B) 1 + 2 + 3 + + ( n ) (C) 1 + 2 + 3 + +(n +1) (D) 1 x 2 x 3 x x ( n _ l)

Q.47 The total energy of a hydrogen atom in its ground state is -13,6eV. If the potential energy in the first excited state is taken as zero then the total energy in the ground state will be :

<L (A) -3.4eV (B) 3.4 eV (C)-6.8eV (D)6.8eV


Q. 48 A neutron collides head on with a stationary hydrogen atom in ground state (A) If kinetic energy of the neutronis less than 13.6eV, collisionmust be elastic (B) if kinetic energy of the neutron is less than 13,6eV, collision may be inelastic. (C) inelastic collision takes place when initial kinetic energy of neutron is greater than 13. 6eV. (D) perfectly inelastic collision cannot take place.

Q. 49 The electron in a hydrogen atom make a transition from an excited state to the ground state. Which of the following statement is true ? (A) Its kinetic energy increases and its potential and total energies decrease (B) Its kinetic energy decreases, potential energy increases and its total energy remains the same. (C) Its kinetic and toal energies decrease and its potential energy increases. (D) its kinetic potential and total energies decreases.

Q. 5 0 The magnitude of angular momentum, orbit radius and frequency of revolution of electron in hydrogen atom corresponding to quantum number n are L, r and f respectively Then according to Bohr's theory of hydrogen atom, (A) fr 2L is constant for all orbits (B) frL is constant for all orbits (C) frL is constant for all orbits (D) frL2 is constant for all orbits

Q.51 In a characteristic X - ray spectra of some atom superimposed on continuous X-ray spectra: f (A) P represents K a line J

C (B) Q represents Kp line J (C) Q and P represents K a and K p lines respectively J (D) Relative positions of K a and K B depend on the particular atom

Q.52 The "K a " X-ray s emission line of tungsten occurs at X = 0.021 nm. The energy difference between K and L levels in this atom is about (A) 0.51 MeV (B) 1.2 MeV (C)59keV (D)13.6eV

Q.53 Consider the nuclear reaction X 2 0 0 > A 1 1 0 + B 9 0

Ifthe binding energy per nucleon for X, AandB is7.4MeV, 8.2. MeV and 8.2 MeV respectively, what is the energy released ? (A) 200 MeV (B) 160 MeV (C) 110 MeV (D) 90 MeV

Q. 54 The binding energy per nucleon for C 1 2 is 7.68 MeV and that for C 1 3 is 7.5 MeV The energy required to remove a neutron from C 1 3 is (A) 5.34 MeV (B) 5.5 MeV (C) 9.5 MeV (D)9.34MeV

Q. 5 5 The binding energies of nuclei X and Y are E L and E 2 respectively. Two atoms of X fuse to give one atom of Y and an energy Q is released. Then: (A) Q = 2Ej -E 2 (B) Q = E 2-2EJ (C)Q = 2 E J + E 2 (D)Q = 2E 2 + EJ

Q. 5 6 Radius of the second Bohr obit of singly ionised helium atom is (A) 0.53 A (B) 1.06 A (C) 0.265 A (D) 0.132 A

Q. 5 7 An electron in Bohr's hydrogen atom has an energy of-3.4 eV. The angular momentum of the electron is (A) h / 7i ' " (B) h / 2TC (C) nh / (n is an integer) (D)2h/7t


Q.58 If each fission in a U 2 3 5 nucleus releases 200 MeV, how many fissions must occurs per second to produce a power of 1 KW (A) 1.325 x 10 1 3 (B)3.125 x 10 1 3 (C) 1.235 x 10 1 3 (D) 2.135 x 10 1 3

Q.59 The rest mass of the deuteron, ] H, is equivalent to an energy of 1876 MeV, the rest mass of a proton is equivalent to 93 9 MeV and that of a neutron to 940 MeV. A deuteron may disintegrate to a proton and a neutron if it : (A) emits a y - ray photon of energy 2 MeV (B) captures ay- ray photon of energy 2 MeV (C) emits a y-ray photon of energy 3 MeV (D) captures a y - ray photon of energy 3 MeV

Q.60 In an a-decay the Kinetic energy of a particle is 48 MeV and Q-value of the reaction is 5 0 MeV. The mass number of the mother nucleus is: (Assume that daughter nucleus is in ground state) (A) 96 (B) 100 (C) 104 (D) none of these

Q.61 In the uranium radioactive series the initial nucleus is 9 2 U 2 3 8 , and the final nucleus is 8 2 Pb 2 0 6 . When the uranium nucleus decays to lead, the number o f a - particles emitted is.. and the number of (3-particles

- emitted... (A) 6, 8 (B) 8, 6 (C) 16, 6 (D) 32, 12

Q.62 The radioactive sources Aand B ofhalf lives of2 hr and 4 hr respectively, initially contain the same number of radioactive atoms. At the end of 2 hours, their rates of disintegration are in the ratio : ( A ) 4 : l (B) 2 : 1 ( C ) V ^ : 1 (D) 1 : 1

Q.63 In a RA element the fraction of initiated amount remaining after its mean life time is 1 ( A ) l - - ( B ) ^ (C) 1 (D) 1 - ~ e

Q. 64 90% of a radioactive sample is left undecayed after time t has elapsed. What percentage of the initialsample will decay in a total time 2t: (A) 20% (B) 19% (C) 40% (D) 38%

Q.65 A radioactive material of half-life T was produced in a nuclear reactor at different instants, the quantity produced second time was twice of that produced first time. If now their present activities are Aj and A 2

respectively then their age difference equals: t

(B)T A , In—-A, In A A,

T In A z

2A, (D)T l n A 2

2A, R, Q.66 Activity of a radioactive substance is Rj at time t j and R^ at time t 2 ( t 2 > t }). Then the ratio ^ is:

£ h ( A ) - (B) e-Mt v+t 2) (C)e f \ - t ^ ll l2 (D) eMti-t 2)

Q.67 There are two radionuclei Aand B. Ais an alpha emitter and B is a beta emitter. Their distintegration constants are in the ratio of 1 : 2. What should be the ratio of number of atoms of two at time t = 0 so that probabilities of getting a and (3 particles are same at time t = 0. (A) 2 : 1 (B) 1 : 2 (C) e (D) e"1


Q.68 The activity of a sample reduces from Aq to A ( ) / yr3 inonehour. The activity after 3 hours more will be A 0 A n A o A 0

2 <A>i7? w - f

Q.69 Halflife of radium is 1620years. How many radium nuclei decay in 5 hours in 5 gm radium? (Atomic weight of radium = 223) (A) 9.1 x 10 1 2 (B) 3.23 x 10 1 5 (C) 1.72 x 10 2 0 ( D ) 3 . 3 x l 0 1 7

Q. 70 Halflife for certain radioactive element is 5 min. Four nuclei of that element are observed at a certain instant of time. After five minutes Assertion (A): It can be definitely said that two nuclei will be left undecayed. Reasoning (R): After halflife i. e. 5 minutes, half of total nuclei will disintegrate. So only two nuclei will be left undecayed. Then (A) A is correct & R is correct explanation of A. (B) Both are correct. But R is not correct explanation of A. (C) A is incorrect & Ris correct. (D) Both are incorrect.

Q. 71 A certain radioactive nuclide of mass number m^ disintegrates, with the emission of an electron and y radiation only, to give second nuclied of mass number m^ Which one of the following equation correctly relates rr^ and m y? (A)m y = m x + 1 (B)m y = m x - 2 (C)m y = m x - 1 (D)m y = m x

Q.72 The number o f a and (3 "emitted during the radioactive decay chain starting from gg6Ra andendingat ^ I? Pb is ( A ) 3 a & 6 p - (B) 4a & 5(3~ ( C ) 5 a & 4 p " ( D ) 6 a & 6 p "

Q.73 The activity ofa sample of radioactive material is A, at time t, and .A, at time t 2 (t 2 >t,). Its mean life is T. A - A (A) Ajt, = A 2t 2 (B) = constant(C) A = A, j w r (D) = \ e(MTt2)

Q. 74 A fraction / , of a radioactive sample decays in one mean life, and a fractionf2 decays in one half-life. (A)/, > / , , ( B ) / , < / ;

/ (C)/ =f2 (D) May be (A), (B) or (C) depending on the values of the mean life and halflife Q.75 A radioactive substance is being produced at a constant rate of 10 nuclei/s. The decay constant ofthe

substance is 1/2 sec"1. After what time the number of radioactive nuclei will become 10? Initially there are no nuclei present. Assume decay law holds for the sample.

1 (A) 2.45 sec (B) log(2) sec (C) 1.386 sec (D) sec

Q.76 The radioactivity o fa sample is R, at time Tj and R 2 at time T 2 . If the halflife of the specimen is T. Number of atoms that have disintegrated in time (T 2 - Tj) is proportional to (A) ( R J , - R 2 T 2 ) (B) (Rj - R , ) T (C) (RJ -R , ) /T (D) (Rj - R,) (T t - T 2 )


Q. 77 The decay constant of the end product of a radioactive series is (A) zero (B) infinite (C) finite (non zero) (D) depends on the end product.

Q. 78 At time t = 0, N, nuclei of decay constant & N, nuclei of decay constant X2 are mixed . The decay rate of the mixture is :

(A) N 1 N 2 e~^ 1 + > " 2 ^

(C) + ( N 1 X 1 e " X l t + N 2 A 2 e " X 2 t ) V N 2 7

(B) +

(D) +N 1 X ] N 2 X 2 e

(x rx 2)t

% Bansal Classes Question Bank on Modern Physics

ONE OR MORE THAN ONE OPTION MAY BE CORRECT Take approx. 3 minutes for answering each question. Q.l In photoelectric effect, stopping potential depends on

(A) frequency of the incident light (B) intensity ofthe incident light by varies source distance (C) emitter's properties (D) frequency and intensity of the incident light

Q. 2 An electron in hydrogen atom first jumps from second excited state to first excited state and then, from first excited state to ground state. Let the ratio of wavelength, momentum and energy of photons in the two cases be x, y and z, then select the wrong answer/(s): (A)z= 1/x (B) x=9/4 (C) y=5/27 (D)z=5/27

Q.3 .An electron is in an excited state in hydrogen-like atom. It has a total energy of-3.4 eV. If the kinetic energy ofthe electron is E and its de-Broglie wavelength is X, then (A) E = 6.8 eV, A, = 6.6 x 10" 1 0 m (B) E = 3.4 eV, X = 6.6 x lO- 1 0 m (C) E = 3.4 eV, X = 6.6 x 10"1 1 m (D) E = 6.8 eV, X = 6.6 x 10"1 1 m

Q.4 A particular hydrogen like atom has its ground state binding "energy 122.4eV. Its is in ground state. Then: (A) Its atomic number is 3 (B) An electron of 90eV can excite it. (C) An electron of kinetic energy nearly 91 8eV can be brought to almost rest by this atom. (D) An electron of kinetic energy 2.6eV may emerge from the atom when electron of kinetic energy

125eV collides with this atom. Q.5 A beam ofultraviolet light of all wavelengths passes through hydrogen gas at room temperature, in the

x-direction. Assume that all photons emitted due to electron transition inside the gas emerge in the y-direction. Let Aand B denote the lights emerging from the gas in the x and y directions respectively. (A) Some of the incident wavelengths will be absent in A. (B) Only those wavelengths will be present in B which are absent in A. (C) B will contain some visible light. (D) B will contain some infrared light.

Q.6 If radiation of allow wavelengths from ultraviolet to infrared is passed through hydrogen agas at room temperature, absorption lines will be observed in the : (A) Lyman series (B) Baimer series (C) both (A) and (B) (D) neither (A) nor (B)

Q.7 In the hydrogen atom, if the reference level of potential energy is assumed to be zero at the ground state level. Choose the incorrect statement. (A) The total energy of the shell increases with increase in the value of n (B) The total energy of the shell decrease with increase in the value of n. (C) The difference in total energy of any two shells remains the same. (D) The total energy at the ground state becomes 13.6 eV.

Q. 8 Choose the correct statement(s) for hydrogen and deuterium atoms (considering motion of nucleus) (A) The radius of first Bohr orbit of deuterium is less than that of hydrogen (B) The speed of electron in the first Bohr orbit of deuterium is more than that of hydrogen. (C) The wavelength of first Balmer line of deuterium is more than that of hydrogen (D) The angular momentum of electron in the first Bohr orbit of deuterium is more than that of hydrogen.


Q.9 Let A n be the area enclosed by the n t h orbit in a hydrogen atom. The graph of In (A n/A,) agains In (n). (A) will pass through origin (B) will be a stright line will slope 4 (C) will be a monotonically increasing nonlinear curve (D) will be a circle.

Q, 10 A neutron collides head-on with a stationary hydrogen atom in ground state. Which of the following statements are correct (Assume that the hydrogen atom and neutron has same mass): (A) If kinetic energy of the neutron is less than 20.4 eV collision must be elastic. (B) If kinetic energy of the neutron is less than 20.4 eV collision may be inelastic. (C) Inelastic collision may be take place only when initial kinetic energy of neutron is greater than 20.4 eV. (D) Perfectly inelastic collision can not take place.

Q.ll When a nucleus with atomic number Z and mass number A undergoes a radioactive decay process: (A) both Z and A will decrease, if the process is a decay (B) Z will decrease but A will not change, ifthe process is p + decay (C) Z will decrease but A will not change, if the process is (3~ decay (D) Z and A will remain unchanged, if the process is y decay.

Q.12 In a Coolidge tube experiment, the minimum wavelength of the continuous X-ray spectrum is equal to 66.3 pm, then (A) electrons accelerate through a potential difference of 12.75 kV in the Coolidge tube (B) electrons accelerate through a potential difference of 18.75 kV inthe Coolidge tube (C) de-Broglie wavelength of the electrons reaching the anti cathode is of the order of 10pm. (D) de-Broglie wavelength of the electrons reaching the anticathode is 0.01 A.

Q.13 The potential difference applied to an X-ray tube is increased. As a result, in the emitted radiation: (A) the intensity increases (B) the minimum wave length increases (C) the intensity decreases (D) the minimum wave length decreases

Q.14 When the atomic number A of the nucleus increases (A) initially the neutron-proton ratio is constant = 1 (B) initially neutron-proton ratio increases and later decreases (C) initially binding energy per nucleon increases and later decreases (D) the binding energy per nucleon increases when the neutron-proton ratio increases.

Q.15 Let m p be the mass of a proton, m n the mass of a neutron, M, the mas ofa ^ N e nucleus and M 2 the mass of a 2[] Ca nucleus. Then (A)M 2 = 2M, (B) M 2 > 2Mj (C) M 2 < 2Mj (D) M, < 10(mn + m p)

Q.16 The decay constant of a radio active substance is 0.173 (years)"1. Therefore : (A) Nearly 63% of the radioactive substance will decay in (1/0.173) year. (B) halflife of the radio active substance is (1/0.173) year. (C) one -forth of the radioactive substance will be left after nearly 8 years. (D) all the above statements are true.

Bansal Classes Question Bank on Modern Physics [15]

ANSWER KEY ONLY ONE OPTION IS CORRECT.

Qi C Q.2 B Q.3 C Q 4 D Q.5 D Q.6 C Q.7 A

Q.8 D Q.9 A Q.10 A Q.ll B Q.12 Q.13 D Q.14 C

Q.15 D Q.16 C Q.17 C Q.18 A Q.19 C Q.20 B Q.21 B

Q.22 B Q.23 A Q.24 B Q.25 A Q.26 A Q.27 B Q.28 C

Q.29 A Q.30 C Q.31 D Q.32 A Q.33 D Q.34 C Q.35 D

Q.36 B Q.37 C Q.38 A Q.39 A Q.40 A Q.41 C Q.42 C

Q.43 C Q.44 D Q.45 C Q.46 B Q.47 C Q.48 A Q.49 A

Q.50 B Q.51 C Q.52 C Q.53 B Q.54 A Q.55 B Q.56 B

Q.57 A Q.58 B Q.59 D Q.60 B Q.61 B Q.62 C Q.63 C

Q.64 B Q.65 C Q.66 D Q.67 A Q.68 B Q.69 B Q.70 D

Q.71 D Q.72 C Q.73 C Q.74 A Q.75 C Q.76 B Q.77 A

Q.78 C ONE OR MORE THAN ONE OPTION MAYBE CORRECT

Q.l A,C Q 2 B Q.3 B Q 4 AC,D Q.5 A,C,D Q.6 A Q.7 B Q.8 A Q.9 AB Q.10 A,C Q.ll AB,D Q.12 B Q.13 A,D Q.14 A,C Q.15 C,D Q.16 A,C

TARGET IIT JEE 2007

XII (ALL)

MODERN PHYSICS

CONTENTS KEYCONCEPTS

EXERCISE-I EXERCISE-II EXERCISE-III ANSWER KEY

KEY CONCEPTS

l. (a) (b) (c) (d)

2.

3.

4.

(0 (ii) (iii) (iv) (v)

(vi)

CATHODE RAYS : Generated in a discharge tube in which a high vaccum is maintained . They are electrons accelerated by high p.d. ( lOto 15 K.V.)

1 K.E. of C.R. particle accelerated by a p.d. V is — mv' Can be deflected by Electric & magnetic fields . ELECTROMAGNETIC SPECTRUM Ordered arrangement of the big family of electro magnetic waves (EMW) either in ascending order of frequencies or of wave lengths Speed ofE.M.W. in vacuum C = 3 x 108 m/s = v X

2m = eV.

red(7.6xl0~ 7m) * — vioIet(3.6*l(r 7 m)

3*10 4 m 3m 3 x l 0 ^ m 3xlO" l 2 m

infrared Ultraviolet Gamma rays

Radio waves

I I X-rays Micro waves \ (e.g. radar) Visible light

104 106 10 s 1 0 1 0 1 0 1 2 1 0 1 4 10 1 6 I0 i 8 10 2 ° Frequency (Hz)

PLANK S QUANTUM THEORY : A beam ofEMW is a stream of discrete packets of energy called PHOTONS ,

each photon having a frequency v and energy = E = h v . h = plank's constant = 6.63 x 10"34 Js . PHOTO ELECTRIC EFFECT : The phenomenon of the emission of electrons , when metals are exposed to light (of a certain minimum frequency) is called photo electric effect. Results : Can be explained only on the basis of the quantum theory (concept of photon). Electrons are emitted ifthe incident light has frequency v > v Q (threshold frequency) emission of electrons is independent of intensity. The wave length corresponding to v 0 is called threshold wave length X0 . v 0 is different for different metals . Number of electrons emitted per second depends on the intensity of the incident light . EINSTEINS PHOTO ELECTRIC EQUATION :

Photon energy = K. E. of electron + work function . 1 2 , h v = — mv + <b 2

(j) = Work function = energy needed by the electron in freeing itself from the atoms of the metal . d> = h v 0

STOPPING POTENTIAL O R CUT O F F PO TENTIAL :

The minimum value of the retarding potential to prevent electron emission is : e Vcutofr = (KE) m a x

Note: The number of photons incident on a surface per unit time is called photon flux. 5. WAVE NATURE OF MATTER :

Beams of electrons and other forms of matter exhibit wave properties including interference and diffraction with a de Broglie wave length given by X = —

P (wave length of a praticle) .

<i§Bansal Classes Modern Physics [11]

6. ATOMIC MODELS : (a) THOMSON MODEL : (PLUM PUDDING MODEL)

(i) Most of the mass and all the positive charge of an atom is uniformly distributed over the full size of atom (10" 1 0m).

(ii) Electrons are studded in this uniform distribution . (iii) Failed to explain the large angle scattering a - particle scattered by thin foils of matter .

(b) RUTHERFORD MODEL : (Nuclear Model) (i) The most of the mass and all the positive charge is concentrated within a size of 10"14 m inside

the atom . This concentration is called the atomic nucleus . (ii) The electron revolves around the nucleus under electric interaction between themin circular orbits.

An accelerating charge radiates the nucleus spiralling inward and finally fall into the nucleus, which does not happen in an atom. This could not be explained by this model .

(c) BOHR ATOMIC MODEL : Bohr adopted Rutherford model of the atom & added some arbitrary conditions. These conditions are known as his postulates : (i) The electron in a stable orbit does not radiate energy .i.e. m V = -r r (ii) A stable orbit is that in which the angular momentum of the electron about nucleus

ll ll is an integral (n) multiple of — . i.e. mvr = n — ; n = 1, 2 , 3 , (n * 0). Z7C 271

(iii) The electron can absorb or radiate energy only if the electron jumps from a lower to a higher orbit or falls from a higher to a lower orbit .

(iv) The energy emitted or absorbed is a light photon of frequency v and of energy. E = hv . FOR HYDROGEN ATOM : (Z - atomic number = 1)

(i) L = angular momentum in the n t h orbit = n — . 2% (ii) r n - radius of n t h circular orbit = (0.529 A 0) n 2 ; (1 A 0 = 10"10 m); r n a n 2. (iii) E n Energy of the electron in the n t h orbit = — e V i.e. E n a .

Note: Total energy ofthe electron in an atom is negative , indicating that it is bound . Binding Energy (BE) = - E = 1 3 , 6 e v . n

(iv) E n 2 - E n l = Energy emitted when an electron jumps from n 2 t h orbit to n, t h orbit (n 2 > n t ) . 1 1 AE = (13.6 ev)

2 2 n , n 2

AE = hv ; v = frequency of spectral line emitted . — = v = wave no. [no. ofwaves in unit length (lm)] = R A, 2 2

n i n 2 Where R = Rydberg's constant for hydrogen = 1.097 x 107 m"1 . (v) For hydrogen like atom/spicies of atomic number Z :

r n 2 = ^ ^ n 2 = (0.529A 0) ^ ; E z = ( - 13.6) ^ ev z Z n R 7 = RZ 2 - Rydberg's constant for element of atomic no. Z .

Note : If motion of the nucleus is also considered, then m is replaced by p. . ^Bansal Classes Modern Physics [3]

Where p = reduced mass of electron - nucleus system = mM/(m+M).

7. (0

00

9.

11. (0 (ii) (iii) (iv)

In this case E„ = (-13.6 ev) — . — n. v 7 o n 2 m e SPECTRAL SERIES : Lyman Series : (Landing orbit n = 1) .

v"=R 1 1 i 2 2 1 n 2

Ultraviolet region Balmer Series : (Landing orbit n = 2)

1 1

n 2 > 1

Visible region v = R 0 2 2 2 n 2

>2

(iii) Paschan Series : (Landing orbit n = 3) In the near infrared region v = R 1 2 r, 2 3 n 2

n 2 > 3

(iv) Bracket Series : (Landing orbit n = 4) In the mid infrared region v = R 4 2

> 4 (v) Pfund Series : (Landing orbit n = 5)

In far infrared region v = R ^ > 5 In all these series n 2 = n, + 1 is the a line

= n, + 2 is the P line = n, + 3 is the y line etc . where n, = Landing orbit

EXCITATION POTENTIAL OF ATOM : Excitation potential for quantum jump from n } -»n 2 electronch arg e IONIZATION ENERGY : The energy required to remove an electron from an atom . The energy required to ionize hydrogen atom is = 0 - ( -13.6) = 13.6 ev .

10. IONIZATION POTENTIAL : Potential difference through which an electron is moved to gain ionization energy = - E .

electronicch arg e X-RAYS : Short wavelength (0.1 A 0 to 1 A 0) electromagnetic radiation . Are produced when a metal anode is bombarded by very high energy electrons . Are not affected by electric and magnetic field . They cause photoelectric emission . Characteristics equation eV = hv m

e = electron charge ; V = accelerating potential v = maximum frequency of X - radiation

k u ~ kp-Characteristic Spectrum

3ntiaous Spectrum

35000 volt


(v) Intensity of X - rays depends on number of electrons hitting the target . (vi) Cut off wavelength or minimum wavelength, where v (in volts) is the p.d. applied to the tube

X J * ! " A" . min - y

(vii) Continuous spectrum due to retardation of electrons. (viii) Characteristic Spectrum due to transition of electron from higher to lower

v a ( z - b ) 2 ; u = a ( z - b ) 2 [ MOSELEY'S LAW ]

b = 1 for K series ; b = 7.4 for L series Where b is Shielding factor (different for different series).

Note : (i) Binding energy=- [ Total Mechanical Energy ] (ii) Vel. of electron in n t h orbit for hydrogen atom = — ; c = speed oflight. 137n

(iii) For x - rays - -R(z-b ) 2

X 1 1 2 2

V n i n 2 J

(iv) Series limit of series means minimum wave length of that series. 1 2 . N U C L E A R D I M E N S I O N S :

R = R 0 A 1 / 3 Where R 0 = empirical constant = 1.1 x 10~15 m; A = Mass number ofthe atom 1 3 . R A D I O A C T I V I T Y :

The phenomenon of self emission of radiation is called radioactivity and the substances which emit these radiations are called radioactive substances . It can be natural or artificial (induced) .

1 4 . a . , p , y R A D I A T I O N :

(i) a - particle : (a) Helium nucleus ( 2 He 4 ) ; (b) energy varies from 4 Mev to 9 Mev; (c) Velocity 106 - 107 m/s ; (d) low penetration

(ii) p - particle : (a) Have much less energy; (b) more penetration; (c) higher velocities than a particles

(iii) y - radiation : Electromagnetic waves of very high energy . 1 5 . L A W S O F R A D I O A C T I V E D I S I N T E G R A T I O N :

(A) DISPLACEMENT LAW : In all radioactive transformation either an a or p particle (never both or more than one of each simultaneously) is emitted by the nucleus of the atom. (i) a-emission : Z X A -> Z _ 2 Y A _ 4 + 2 a 4 + Energy (ii) P - emission : Z X A > P+ Z + 1 Y A + v (antinuetrino) (iii) y - emission : emission does not affect either the charge number or

the mass number . ( B ) STASTISTICAL LAW : The disintegration is a random phenomenon. Whcih atom disintegrates first is

purely a matter of chance . Number of nuclei disintegrating per second is given ; (disintegration /s/gm is called specific activity) . 0 dN X T dN , X T (i) — a N —>—=-A,N = activity . dt dt

Where N = No. of nuclei present at time t ; X - decay constant (ii) N = N o e~ N 0 = number of nuclei present in the beginning .


(iii) Half life of the population T 1 / 2 = • A N at the end of n half-life periods the number of nuclei left N = — .

. . . . , Slifetimeof allatoms „ 1 ( i v ) MEAN LIFE OF AN ATOM = ; T = — totalnumberof atoms A (v) CURIE : The unit of activity of any radioactive substance in which the number of disintegration

per second is 3.7 xlO 1 0 . 16. ATOMIC MASS UNIT (a.m.u. OR U) :

1 amu = — x (mass of carbon-12 atom) = 1.6603 x 10~27 kg

17. MASS AND ENERGY : The mass m of a particle is equivalent to an energy given by E = mc 2 ; c = speed of light. 1 amu = 931 Mev

18. MASS DEFECT AND BINDING ENERGY OF A NUCLEUS : The nucleus is less massive than its constituents. The difference of masses is called mass defect . A M = mass defect = [ Z M P + ( A - Z ) m J - M ^ .

Total energy required to be given to the nucleus to tear apart the individual nucleons compos ing the nucleus, away from each other and beyond the range of interaction forces is called the Binding Energy of a nucleus . BE. = ( A M ) C 2 .

( A M ) C 2 B E. per nucleon = - — ~ — . Greater the BE. , greater is the stability of the nucleus .

19. NUCLEAR FISSION : (i) Heavy nuclei of A, above 200, break up onto two or more fragments of comparable masses. (ii) The total B.E. increases and excess energy is released . (iii) The man point of the fission energy is leberated in the form ofthe K.E. ofthe fission fragments

. eg. 2 9 2 U + o n l ^ 2 9 2 U ^ I 5 4 6 B a + 3 6 K r + 3 o n l + ^ S Y 20. NUCLEAR FUSION (Thermo nuclear reaction): (i) Light nuclei ofAbelow 20, fuse together, the BE. per nucleon increases and hence the excess energy

is released . (ii) These reactions take place at ultra high temperature (= 107 to 109) (iii) Energy released exceeds the energy liberated in the fission of heavy nuclei .

eg. 4{P-»j 1He+° 1e . (Positron) (iv) The energy released in fusion is specified by specifying Q value .

i.e. Q value of reaction = energy released in a reaction . Note : (i) In emission of p", z increases by 1 .

(ii) In emission of , z decreases by 1 .


EXERCISE # I Q.l A parallel beam of uniform, monochromatic light of wavelength 2640 A has an intensity of

200W/m2. The number of photons in 1mm3 of this radiation are Q. 2 When photons of energy 4.25 eV strike the surface of a metal A, the ej ected photoelectrons have maximum

kinetic energy T a eV and de Broglie wavelength Xa. The maximum kinetic energy of photoelectrons

liberated from another metal B by photons of energy 4.7eV is T b = (T -1 .5) eV. If the De Broglie wavelength of these photoelectrons is = 2 X

&, then find

(a) The work function of a (b) The work function of b is (c) T a and T b

Q.3 When a monochromatic point source oflight is at a distance of 0.2 m from a photoelectric cell, the cut off voltage and the saturation current are respectively 0.6 volt and 18.0 mA. Ifthe same source is placed 0.6 m away from the photoelectric cell, then find

(a) the stopping potential (b) the saturation current Q.4 An isolated metal body is illuminated with monochromatic light and is observed to become charged to

a steady positive potential 1.0V with respect to the surrounding. The work function of the metal is 3 0 eV. The frequency of the incident light is .

Q. 5 663 mW oflight from a 540 nm source is incident on the surface of a metal. If only 1 of each 5 x 109

incident photons is absorbed and causes an electron to be ejected from the surface, the total photocurrent in the circuit is .

Q. 6 Light of wavelength 330 nm falling on a piece of metal ej ects electrons with sufficient energy which requires voltage V 0 to prevent a collector. In the same setup, light of wavelength 220 nm, ej ects electrons which require twice the voltage V 0 to stop them in reaching a collector. Find the numerical value of voltage V0.(Take plank's constant, h = 6.6 x i c r 3 4 Js and 1 eV= 1.6 x 10~19 J)

Q.7 A hydrogen atom in a state having a binding energy 0.85eV makes a transition to a state of excitation energy 10.2eV. The wave length of emitted photon is nm.

Q.8 A hydrogen atom is in 5 t h excited state. When the electron jumps to ground state the velocity of recoiling hydrogen atom is m/s and the energy of the photon is eV.

Q. 9 The ratio of series limit wavlength ofBalmer series to wavelength of first line of paschen series is Q.10 An electron joins a helium nucleus to form a He+ ion. The wavelength ofthe photon emitted in this process

if the electron is assumed to have had no kinetic energy when it combines with nucleus is nm. Q.ll Three energy levels of an atom are shown in the figure. The wavelength

corresponding to three possible transition are A,, X2 and X

y The value E?-

o f X3 in terms of A, and X

2 is given by .

Xi x2

- n = 2

Q.12 Imagine an atom made up of a proton and a hypothetical particle of double the mass of an electron but having the same charge as the electron. Apply the Bohr atom model and consider a possible transitions of this hypothetical particle to the first excited level. Find the longest wavelngth photon that will be emitted X (in terms of the Rydberg constant R.)

Q.13 In a hydrogen atom, the electron moves in an orbit of radius 0.5 A making 10 1 6 revolution per second. The magnetic moment associated with the orbital motion of the electron is .

Q.14 The positron is a fundamental particle with the same mass as that ofthe electron and with a charge equal to that of an electron but of opposite sign. When a positron and an electron collide, they may annihilate each other. The energy corresponding to their mass appears in two photons of equal energy. Find the wavelength of the radiation emitted. [Take : mass ofelectron = (0.5/C 2)MeVandhC= 1.2xlO~ I 2MeV.m where his the Plank's constant and C is the velocity oflight in air]


Q.15 Asmall 10W source of ultraviolet light ofwavelength 99 nm is held at a distance 0.1 mfromametal surface. The radius of an atom ofthe metal is approximately 0.05 nm. Find

(i) the average number of photons strildng an atom per second. (ii) the number ofphotoelectrons emitted per unit area per second ifthe efficiency ofliberation ofphotoelectrons is 1 %. Q.16 The surface of cesium is illuminated with monochromatic light of various

wavelengths and the stopping potentials for the wavelengths are measured. The results of this experiment is plotted as shown in the figure. Estimate the value of work function of the cesium and Planck's constant.

Q.17 A hydrogen like atom has its single electron orbiting around its stationary nucleus. The energy to excite the electron from the second Bohr orbit to the third Bohr orbit is 47.2 eV. The atomic number of this nucleus is .

Q.18 A single electron orbits a stationary nucleus of charge Ze where Z is a constant and e is the electronic charge. It requires 47.2eV to excite the electron from the 2nd Bohr orbit to 3rd Bohr orbit. Find

(i) the value of Z, (ii) energy required to excite the electron from the third to the fourth orbit (iii) the wavelength of radiation required to remove the electron from the first orbit to infinity (iv) the kinetic energy, potential energy and angular momentum in the first Bohr orbit (v) the radius of the first Bohr orbit. Q .19 A hydrogen like atom (atomic number Z) is in higher excited state of quantum number n. This excited

atom can make a transition to the first excited state by successively emitting two photons of energy 22.95 eV and 5.15eV respectively. Alternatively, the atom from the same excited state can make transition to the second excited state by successively emitting two photons of energies 2.4eV and 8.7eV respectively. Find the values of n and Z.

Q.20 Find the binding energy of an electron in the ground state of a hydrogen like atom in whose spectrum the third of the corresponding B aimer series is equal to 108. 5nm.

Q.21 Which level of the doubly ionized lithium has the same energy as the ground state energy of the hydrogen atom. Find the ratio ofthe two radii of corresponding orbits.

Q.22 The binding energies per nucleon for deuteron (jH 2 ) and helium ( 2 He 4 ) are 1.1 MeV and 7.0 MeV respectively. The energy released when two deuterons fuse to form a. helium nucleus ( 2He 4) is .

Q.23 Aradioactive decay counter is switched on at t = 0. A P - active sample is present near the counter. The counter registers the number of P - particles emitted by the sample. The counter registers 1 x 10' P - particles at t = 36 s and 1.11 * 10s P - particles at t = 108 s. FindT, of this sample

Q.24 An isotopes of Potassium has a half life of 1.4 x 109 year and decays to Argon ^ A r which is stable. (i) Write down the nuclear reaction representing this decay. (ii) A sample of rock taken from the moon contains both potassium and argon in the ratio 1 /7. Find age of

rock Q.25 At t = 0, a sample is placed in a reactor. An unstable nuclide is produced at a constant rate R in the

sample by neutron absorption. This nuclide P~~ decays with halflife x. Find the time required to produce 80% of the equilibrium quantity of this unstable nuclide.

Q.26 Suppose that the Sun consists entirely of hydrogen atom and releases the energy by the nuclear reaction, 4 |H > ,He with 26 MeV of energy released. Ifthe total output power of the Sun is assumed to remain constant at 3.9 x 10 2 6 W, find the time it will take to burn all the hydrogen. Take the mass of the Sun as 1.7 x 10 3 0 kg.

f 2-1 1-0 .41

I-.-7 1-2V 1.5 1.0 1.5 V I O ' 5 H Z


Q. 27 Assuming that the source of the energy of solar radiation is the energy of the formation of helium from hydrogen according to the following cyclic reaction : C' 2 + ,H' 7 N 1 3 X 1 3 + e° 6 1 / o + l

,C 1 3 + ,H' N 1 4 0 1 / 7 N 1 4 + ,H1 8 0 1 5 -> 7 N 1 5 + + 1e°

7 N 1 5 + ] H 1 -> 6 C 1 2 + 2He 4

Find how many tons of hydrogen must be converted every second into helium . The solar constant is 8 J / cm2 min. Assume that hydrogen forms 35% of the sun's mass. Calculate in how many years this hydrogen will be used up if the radiation of the sun is constant. m e = 5.49 x 10 4 amu, atomic masses m^l .00814 amu, mH e=4.00388 amu, mass ofthe sun=2 x 103 0 kg, distance between the sun and the earth= 1.5* 10 nm. 1 amu = 931 MeV.

Q. 28 An electron of mass "m" and charge "e" initially at rest gets accelerated by a constant electric field E. The rate of change of DeBroglie wavelength of this electron at time t is

List of recommended questions from I.E. Irodov. 5.247, 5.249, 5.260, 5.262, 5.263, 5.264, 5.265, 5.266, 5.270, 5.273, 5.277 6.21, 6.22, 6.27, 6.28, 6.30, 6.31, 6.32, 6.33, 6.35, 6.37, 6.38, 6.39, 6.40, 6.41, 6.42, 6.43, 6.49, 6.50, 6.51, 6.52, 6.53, 6.133, 6.134, 6.135, 6.136,

6.137, 6.138, 6.141, 6.214, 6.233, 6.249, 6.264, 6.289

EXERCISE # II Q.l Find the force exerted by a light beam of intensity I, incident on a cylinder I

(height h and base radius R) placed on a smooth surface as shown in figure if: • (a) surface of cylinder i s perfectly reflecting > (b) surface of cylinder is having reflection coefficient 0.8. (assume no »

transmission) t —

Q. 2 A small plate of a metal (work function =1.17 eV) is placed at a distance of 2m from a monochromatic light source of wave length 4.8 * 10"7 m and power 1.0 watt. The light falls normally on the plate. Find the number of photons striking the metal plate per square meter per sec. If a constant uniform magnetic field of strength A tesla is applied parallel to the metal surface. Find the radius of the largest circular path followed by the emitted photoelectrons.

Q. 3 Electrons in hydrogen like atoms (Z = 3) make transitions from the fifth to the fourth orbit & from the fourth to the third orbit. The resulting radiations are incident normally on a metal plate & eject photo electrons. The stopping potential for the photoelectrons ejected by the shorter wavelength is 3.95 volts. Calculate the work function of the metal, & the stopping potential for the photoelectrons ejected by the longer wavelength. (Rydberg constant = 1.094 x 107 m 1 )

Q.4 A beam of light has three wavelengths 4144A, 4972A & 6216 A with a total intensity of 3.6x 10"3 W. m 2 equally distributed amongst the three wavelengths. The beam falls normally on an area 1.0 cm2 of a clean metallic surface of work function 2.3 eV. Assume that there is no loss of light by reflection and that each energetically capable photon ejects one electron. Calculate the number of photoelectrons liberated in two seconds.


Q. 5 Monochromatic radiation of wavelength = 3 000A falls on a photocell operating in saturating mode. The corresponding spectral sensitivity of photocell is J = 4.8 x 10~3 A/w. When another monochromatic radiation of wavelength X2 = 1650A and power P = 5 x 10~3 W is incident, it is found that maximum velocity of photoelectrons increases n = 2 times. Assuming efficiency of photoelectron generation per incident photon to be same for both the cases, calculate

(i) threshold wavelength for the cell. , (ii) saturation current in second case.

Q.6 A monochromatic point source S radiating wavelength 6000 A with A SC power 2 watt, an aperture A of diameter 0.1 m & a large screen SC are placed as shown in figure. Aphotoemissive detector D of surface area S 0.5 cm2 is placed at the centre ofthe screen. The efficiency of the detector for the photoelectron generation per incident photon is 0.9.

(i) Calculate the photon flux density at the centre of the screen and the p.6 m photocurrent in the detector. 6 m

D

(ii) If a concave lens L of focal length 0.6 m is inserted in the aperture as shown, find the new values of photon flux density & photocurrent .Assume a uniform average transmission of 80% for the lens.

(iii) If the work-function of the photoemissive surface is 1 eV, calculate the values of the stopping potential in the two cases (without & with the lens in the aperture).

Q.7 A small 10 W source of ultraviolet light of wavelength 99 nm is held at a distance 0.1m from a metal surface. The radius of an atom ofthe metal is approximaterly 0.05 nm. Find :

(i) the number of photons striking an atom per second. (ii) the number of photoelectrons emitted per second if the efficiency of liberation of photoelectrons is 1 %

Q.8 A neutron with kinetic energy 25 eV strikes a stationary deuteron. Find the de Broglie wavelengths of both particles in the frame of their centre of mass.

Q. 9 Two identical nonrelativistic particles move at right angles to each other, possessing De Broglie wavelengths, A, & Xj . Find the De Broglie wavelength of each particle in the frame of their centre of mass.

Q.10 A stationary He+ ion emitted a photon corresponding to the first line its Lyman series. That photon liberated a photoelectron from a stationary hydrogen atom in the ground state. Find the velocity of the photoelectron.

Q.ll A gas of identical hydrogen like atoms has some atoms in the lowest (ground) energy level A & some atoms in a particular upper (excited) energy level B& there are no atoms in any other energy level. The atoms of the gas make transition to a higher energy level by the absorbing monochromatic light of photon energy 2.7eV Subsequently, the atoms emit radiation of only six different photon energies. Some of the emitted photons have energy 2.7 eV. Some have energy more and some have less than 2.7 eV.

(i) Find the principal quantum number of the initially excited level B. (ii) Find the ionisation energy for the gas atoms. (iii) Find the maximum and the minimum energies of the emitted photons. Q.12 A hydrogen atom in ground state absorbs a photon of ultraviolet radiation ofwavelength 50 nm. Assuming that

the entire photon energy is taken up by the electron, with what kinetic energy will the electron be ejected ?

Q.13 A monochromatic light source of frequency v illuminates a metallic surface and ej ects photoelectrons. The photoelectrons having maximum energy are just able to ionize the hydrogen atoms in ground state. When the whole experiment is repeated with an incident radiation of frequency (5/6)v, the photoelectrons so emitted are able to excite the hydrogen atom beam which then emits a radiation of wavelength of 1215 A. Find the work function of the metal and the frequency v.


Q . 14 An energy of 68.0 eV is required to excite a hydrogen like atom from its second Bohr orbit to the third. The nuclear charge Ze. Find the value of Z, the kinetic energy of the electron in the first Bohr orbit and the wavelength of the electro magnetic radiation required to eiect the electron from the first Bohr orbit to infinity.

Q.15 A classical model for the hydrogen atom consists of a single electron of mass rn, in circular motion of radius r around the nucleus (proton). Since the electron is accelerated, the atom continuously radiates electromagnetic waves. The total power P radiated by the atom is given by P = Po/r 4 where

e 6 P o = Q , J c 3 r 3 m 2 (C = velocity oflight) u yon £q L, m e

(i) Find the total energy of the atom. (ii) Calculate an expression for the radius r (t) as a function of time. Assume that at t=0, the radius is rQ = 10"10 m. (iii) Hence or otherwise find the time t 0 when the a

Take •o

1 = r « 3 x l 0 ~ 1 5 m V3 4 n s 0 m e C 2 e

om collapses in a classical model ofthe hydrogen atom.

-M

Q.16 Simplified picture of electron energy levels in a certain atom is shown in the figure. The atom is bombarded with high energy electrons. The impact of one of these electron has caused the complete removal of K-level is filled by an electron from the L-level with a certain amount of energy being released during the transition. This energy may appear as X-ray or may all be used to eject an M-level electron from the atom. Find : ~3* 1 0 - 1 5 J

(i) the minimum potential difference through which electron may be accelerated from rest to cause the ejectrion of K-level electron from the atom.

(ii) energy released when L-level electron moves to fill the vacancy in the K-level. (iii) wavelength of the X-ray emitted. (iv) K.E. of the electron emitted from the M-level.

Q. 17 U 2 3 8 and U 2 3 3 occur in nature in an atomic ratio 140 :1. Assuming that at the time of earth's formation the two isotopes were present in equal amounts. Calculate the age of the earth. (Halflife o f u 2 3 8 = 4.5 x lo 9 yrs & that o f U 2 3 5 = 7.13 x l o 8 yrs)

Q.18 The kinetic energy of an a - particle which flies out of the nucleus of a R a 2 2 6 atom in radioactive disintegration is 4.78 MeV. Find the total energy evolved during the escape of the a - particle.

Q.19 A small bottle contains powdered beryllium Be & gaseous radon which is used as a source of a-particles. Neutrons areproduced whena-particlesoftheradonreact with beryllium. The yield ofthis reaction is (1/4000) i.e. only one a-particle out of4000 induces the reaction. Find the amount of radon (Rn 2 2 2) originally introduced into the source, if it produces 1.2x 106 neutrons per second after 7.6 days. [ T 1 7 o f R n = 3 . 8 days]

Q.20 An experiment is done to determine the half-life of radioactive substance that emits one p-particle for each decay process. Measurement show that an average of 8.4 P are emitted each second by 2.5 mg ofthe substance. The atomic weight ofthe substance is 230. Find the halflife ofthe substance.

Q.21 When thermal neutrons (negligible kinetic energy) are used to induce the reaction; 5°B + | 3n ——» 3 Li + j He • ot - particles are emitted with an energy of 1.83 MeV.

Given the masses of boron neutron & He 4 as 10.01167,1.00894 & 4.003 86 u respectively. What is the mass of 3 Li ? Assume that particles are free to move after the collision.


Q.22 In a fusion reactor the reaction occurs in two stages : (i) Twodeuterium (2D) nuclei fuse to form a tritium ( T) nucleus with a proton as product. The reaction

may be represented as D (D, p) T. (ii) A tritium nucleus fuses with another deuterium nucleus to form a helium ( 4 He) nucleus with neutron as

another product. The reaction is represented as T(D, n) a . Find : (a) The energy release in each stage . (b) The energy release in the combined reaction per deuterium & (c) What % of the mass of the initial deuterium is released in the form of energy.

Given: (fE>) = 2.014102u ; ( 3 t ) = 3.016049u ; He) = 4.002603 u ; (}p)= 1.00785 u ; (j,n)= 1.008665 u

Q.23 A wooden piece of great antiquity weighs 50 gm and shows C 1 4 activity of320 disintegrations per minute. Estimate the length of the time which has elapsed since this wood was part of living tree, assuming that living plants show a C 1 4 activity of 12 disintegrations per minute per gm. The halflife of C 1 4 is 5730 yrs.

Q.24 Show that in a nuclear reaction where the outgoing particle is scattered at an angle of 90° with the direction of the bombarding particle, the Q-value is expressed as

Q = K P v l v i o ) - K I f \ l + m > v M o ;

Where, I = incoming particle, P = product nucleus, T = target nucleus, O = outgoing particle. Q.25 When Lithium is bombarded by 10 MeV deutrons, neutrons are observed to emerge at right angle to the

direction of incident beam. Calculate the energy of these neutrons and energy and angle of recoil of the associated Beryllium atom. Given that : m ( 0 n ] ) = 1.00893 amu ; m ( 3 Li 7 ) = 7.01784 amu ; m (jH 2 ) = 2.01472 amu ; and m ^Be 8 ) =.8.00776 amu.

Q.26 A body of mass m 0 is placed on a smooth horizontal surface. The mass of the body is decreasing exponentially with disintegration constant X. Assuming that the mass is ejected backward with a relative velocity v. Initially the body was at rest. Find the velocity of body after time t.

Q.27 A radionuclide with disintegration constant X is produced in a reactor at a constant rate a nuclei per sec. During each decay energy E 0 is released. 20% of this energy is utilised in increasing the temperature of water. Find the increase in temperature of m mass of water in time t. Specific heat of water is S. Assume that there is no loss of energy through water surface.


EXERCISE # III Q.l A neutron of kinetic energy 65 eV collides inelastically with a singly ionized helium atom at rest. It is

scattered at an angle of 90° with respect of its original direction. (i) Find the allowed values of the energy ofthe neutron & that ofthe atom after collision. (ii) If the atom gets de-excited subsequently by emitting radiation, find the frequencies of the emitted radiation.

(Given: Mass ofhe atom = 4x(mass ofneutron), ionization energy ofH atom=13.6 eV) [JEE '93] Q.2 A hydrogen like atom (atomic number Z) is in a higher excited state of quantum number n. This excited

atom can make a transition to the first excited state by successively emitting two photon s of energies 10.20 eV & 17.00 eV respectively. Alternatively, the atom from the same excited state can make a transition to the second excited state by successively emitting two photons of energies 4.25 eV& 5.95 eV respectively. Determine the values of n&Z. (Ionisation energy of hydrogen atom = 13.6eY)[JEE'94]

Q. 3 Select the correct alternative(s): When photons of energy 4.25 eV strike the surface of a metal A, the ejected photo electrons have maximum kinetic energy T A eV and de-Broglie wave length yA. The maximum kinetic energy of photo electrons liberated from another metal B by photons of energy 4.70 eV is T B = (T A-1.50) eV. If the de-Broglie wave length of these photo electrons is y B = 2yA, then : (A) the work function of A is 2.225 eV (B) the work function ofB is 4 20 eV (C) Ta = 2.00 eV (D) T B = 2.75 eV [JEE'94]

Q.4 In a photo electric effect set-up, a point source of light of power 3.2 x 10"3 W emits mono energetic photons of energy 5.0 eV. The source is located at a distance of 0.8 m from the centre of a stationary metallic sphere of work function 3.0 eV&of radius 8.0 x 10" 3m.The efficiency of photoelectrons emission is one for every 106 incident photons. Assume that the sphere is isolated and initially neutral, and that photo electrons are instantly swept away after emission.

(a) Calculate the number of photo electrons emitted per second. (b) Find the ratio of the wavelength of incident light to the De-Broglie wavelength ofthe fastest photo

electrons emitted. (c) It is observed that the photo electron emission stops at a certain time t after the light source is switched

on. Why ? (d) Evaluate the time t. [JEE' 95] Q.5 An energy of 24.6 eV is required to remove one of the electrons from a neutral helium atom. The

energy (In eV) required to remove both the electrons form a neutral helium atom is : (A) 38.2 (B) 49.2 (C) 51.8 (D) 79.0 [JEE'95]

Q.6 An electron, in a hydrogen like atom, is inanexcitedstate. l t has a total energy o f - 3 . 4 eV. Calculate: (i) The kinetic energy & (ii) The De - Broglie wave length of the electron. [JEE 96]

/1 g Q.7 An electron in the ground state of hydrogen atoms is revolving in fi\

anti-clockwise direction in a circular orbit of radius R. (i) Obtain an expression for the orbital magnetic dipole moment of the electron. / ^ (ii) The atom is placed in a uniform magnetic induction, such that the plane normal

to the electron orbit make an angle of 3 0° with the magnetic induction. Find \ the torque experienced by the orbiting electron. [JEE'96]

Q.8 A potential difference of 20 KV is applied across an x-raytube. The minimum wave length ofX-rays generated is . [JEE'96]


Q. 9(i) As per Bohr model, the minimum energy (in eV) required to remove an electron from the ground state of doubly ionized Li atom (Z = 3) is (A) 1.51 (B) 13.6 (C) 40.8 (D) 122.4

(ii) Assume that the de-Broglie wave associated with an electron can form a standing wave between the atoms arranged in a one dimensional array with nodes at each of the atomic sites, It is found that one such standing wave is formed if the distance'd' between the atoms of the array is 2 A. A similar standing wave is again formed if 'd'is increased to 2.5 Abut not for any intermediate value of d. Find the energy ofthe electrons in electron volts and the least value of d for which the standing wave ofthe type described above can form. [JEE 97]

Q. 10(i) The work function of a substance is 4.0 eV. The longest wavelength oflight that can cause photoelectron emission from this substance is approximately: (A) 540 nm (B) 400nm (C) 310nm (D) 220nm

(ii) The electron in a hydrogen atom makes a transition n, > r^, where n, & n 2 are the principal quantum numbers of the two states. Assume the Bohr model to be valid . The time period ofthe electron in the initial state is eight times that in the final state. The possible values of n } & n 2 are: (A) ^ = 4,112 = 2 ( B ) n t = 8 , ^ = 2 (C) n, = 8, r^ = 1 (D) n, = 6, r^ = 3 [JEE '98]

Q.ll A particle of mass M at rest decays into two particles of masses m l and m 2, having non-zero velocities. The ratio of the de-Broglie wavelengths of the particles, A.,/ X2, is ( A)m

l/m

2 { B ) m

2/ m

x ( C ) 1 .0 ~ ( D ) ^ l m

2N m

l [ J E E ' 9 9 ]

Q.12 Photoelectrons are emitted when 400 nm radiation is incident on a surface of work function 1. 9e V. These photoelectrons pass through a region containing a-particles. Amaximum energy electron combines with an a-particle to form a He + ion, emitting a single photon in this process. He + ions thus formed are in their fourth excited state. Find the energies in eV of the photons, lying in the 2 to 4eV range, that are likely to be emitted during and after the combination. [Take, h = 4.14 x 10"15 eV-s] [JEE'99]

Q. 13(a) Imagine an atom made up of a proton and a hypothetical particle of double the mass ofthe electron but having the same charge as the electron. Apply the Bohr atom model and consider all possible transitions of this hypothetical particle to the first excited level. The longest wavelength photon that will be emitted has wavelength X (given in terms of the Rydberg constant R for the hydrogen atom) equal to (A) 9/(5R) (B) 36/(5R) (C) 18/(5R) (D)4/R [JEE'2000 (Scr)]

(b) The electron in a hydrogen atom makes a transition from an excited state to the ground state. Which of the following statements is true? (A) Its kinetic energy increases and its potential and total energies decrease. (B) Its kinetic energy decreases, potential energy increases and its total energy remains the same. (C) Its kinetic and total energies decrease and its potential energy increases. (D) Its kinetic, potential and total energies decrease. [JEE' 2000 (Scr)]

Q.l 4(a) A hydrogen-like atom of atomic number Z is in an excited state of quantum number 2 n. It can emit a maximum energy photon of204 eV. If it makes a transition to quantum state n, a photon of energy 40.8 eV is emitted. Find n, Z and the ground state energy (in eV) for this atom. Also, calculate the minimum energy (in eV) that can be emitted by this atom during de-excitation. Ground state energy of hydrogen atom is -13 .6 eV. [JEE12000]

(b) When a beam of 10.6 eV photon of intensity 2 W/m 2 falls on aplatinum surface of area 1 x 104 m 2 and work function 5.6 ev, 0.53% of the incident photons eject photoelectrons. Find the number of photoelectrons emitted per sec and their minimum and maximum energies in eV. [JEE' 2000]


Q.15 The potential difference applied to an X - ray tube is 5 kV and the current through it is 3.2 mA. Then the number of electrons striking the target per second is [JEE' 2002 (Scr.)] (A) 2 x 10 1 6 (B) 5 x 10 1 6 ( C ) l x l O 1 7 (D) 4 x 10 1 5

Q.16 A Hydrogen atom and Li + + ion are both in the second excited state. If l E and l u are their respective electronic angular momenta, and E R and E L i their respective energies, then (A) / H > l u and |E H | > |E U | (B) / H = l u and |E H | < | E J (C) / H = l u and-|EH| > | E J (D) / h < l u and IEJ < | E J [JEE 2002 (Scr)]

Q.17 A hydrogen like atom (described by the Bohr model) is observed to emit six wavelengths, originating from all possible transition between a group oflevels. These levels have energies between - 0.85 eV and - 0.544 eV (including both these values)

(a) Find the atomic number ofthe atom. (b) Calculate the smallest wavelength emitted in these transitions. [JEE' 2002] Q.18 Two metallic plates A and B each of area 5 x 10 - 4 m 2, are placed at a separation of 1 cm. Plate B carries

a positive charge of33.7 x 10~ ! 2C. A monochromatic beam oflight, with photons of energy 5 eV each, starts falling on plate A at t = 0 so that 10 1 6 photons fall on it per square meter per second. Assume that one photoelectron is emitted for every 106 incident photons. Also assume that all the emitted photoelectrons are collected by plate B and the work function of plate Aremains constant at the value 2 eV. Determine

(a) the number of photoelectrons emitted up to t = 10 sec. (b) the magnitude of the electric field between the plates A and B at t = 10 s and (c) the kinetic energy of the most energetic photoelectron emitted at t = 10 s when it reaches plate B.

(Neglect the time taken by photoelectron to reach plate B) [JEE' 2002] Q.19 The attractive potential for an atom is given by v = v 0 In (r / r 0 ) , v 0 and rQ are constant and r is the radius

of the orbit. The radius r of the n t h Bohr's orbit depends upon principal quantum number n as : (A)rocn (B) r°c 1/n2 ( C ) r x n 2 (D)roc 1/n

[JEE' 2003 (Scr)] Q. 20 Frequency of a photon emitted due to transition of electron of a certain elemrnt from L to K shell is

found to be 4.2 x 10 1 8 Hz. Using Moseley's law, find the atomic number of the element, given that the Rydberg's constant R = 1.1 x 107 mr1. [JEE 2003]

Q.21 In a photoelctric experiment set up, photons of energy 5 eV falls on the cathode having work function 3 eV (a) If the saturation current is i A = 4pA for intensity 10~5 W/m2, then plot a graph between anode potential

and current. (b) Also draw a graph for intensity of incident radiation of 2 x 10" 5W/m 2? [JEE'2003] Q.22 A star initially has 10 4 0 deutrons. It produces energy via, the processes } H 2 + jH 2 —>• jH 3 + p

& jH 2 +,H 3 -» 2 He 4 +n. If the average power radiated by the star is 10 1 6 W, the deuteron supply of the star is exhausted in a time of the order of: [JEE' 93 ] (A) 106 sec (B) 108 sec (C) 10 1 2 sec (D)10 1 6 sec

Q. 23 A small quantity of solution containing 2 4 Na radionuclide (halflife 15 hours) of activity 1.0 microcurie is injected into the blood of a person. A sample ofthe blood of volume 1 cm 3 taken after 5 hours shows an activity of296 disintegrations per minute. Determine the total volume of blood in the body of the person. Assume that the radioactive solution mixes uniformly in the blood of the person. (1 Curie = 3.7 x 10 1 0 disintegrations per second) [JEE'94]

Q.24(i)Fast neutrons can easily be slowed down by : (A) the use of lead shielding (B) passing them through water (C) elastic collisions with heavy nuclei (D) applying a strong electric field


(ii) Consider a-particles, P - particles&y rays, each having an energy of 0.5 MeV. Increasing order of penetrating powers, the radiations are : [JEE'94] (A) a , P , y (B) a , y , (3 ( C ) ( 3 , y , a ( D ) y , p , a

Q. 2 5 Which of the following statement(s) is (are) correct ? [JEE'94] (A) The rest mass of a stable nucleus is less than the sum of the rest masses of its separated nucleons. (B) The rest mass of a stable nucleus is greater than the sum of the rest masses of its separated nucleons. (C) In nuclear fusion, energy is released by fusion two nuclei of medium mass (approximately 100 amu). (D) In nuclear fission, energy is released by fragmentation of a very heavy nucleus.

Q.26 The binding energy per nucleon of 160 is 7.97 MeV & that of ,70 is 7.75 MeV. The energy in MeV required to remove a neutron from 170 is : [JEE'95] (A) 3.52 (B) 3.64 (C) 4.23 (D) 7.86

Q.27 At a given instant there are 25 % undecayed radio-active nuclei in a sample. After 10 sec the number of undecayed nuclei remains to 12.5 % . Calculate : [JEE 96]

(i) mean - life of the nuclei and (ii) The time in which the number of undecayed nuclear will further reduce to 6.25 % of the reduced number. Q.28 Consider the following reaction ; ^ ^ H , = 4 He 2 + Q . [JEE 96]

Mass ofthe deuterium atom = 2.0141 u ; Mass ofthe helium atom = 4.0024 u This is a nuclear reaction in which the energy Q is released is MeV.

Q.29(a)The maximum kinetic energy of photoelectrons emitted from a surface when photons of energy 6 eV fall on it is 4 eV The stopping potential in Volts is : (A) 2 (B) 4 (C) 6 (D) 10

(b) In the following, column I lists some physical quantities & the column II gives approx. energy values associated with some of them. Choose the appropriate value of energy from column II for each ofthe physical quantities in column I and write the corresponding letter A, B, C etc. against the number (i), (ii), (iii), etc. of the physical quantity in the answer book. In your answer, the sequence of column I should be maintained.

Column I Column II (i) Energy of thermal neutrons (A) 0.025 e V (ii) Energy of X-rays (B) 0.5 eV (iii) Binding energy per nucleon (C) 3 eV (iv) Photoelectric threshold of metal (D) 20 eV

(E)10keV (F) 8 MeV

(c) The element Curium Cm has a mean life of 10 1 3 seconds. Its primary decay modes are spontaneous fission and a decay, the former with a probability of 8% and the latter with a probability of 92%. Each fission releases 200 MeV of energy. The masses involved in a decay are as follows :

2ggCm=248.072220u,2^Pu=244.0641 OOu&jHe =4.002603u. Calculate the power output from a sample of 10 2 0 Cm atoms. (1 u = 931 MeV/c 2) [JEE'97]

Q.30 Select the correct alternative(s) . [JEE'98] (i) Let m p be the mass of a proton, m n the mass of a neutron, M, the mass of a ^Ne nucleus & M 2 the

mass of a ^Ca nucleus. Then : (A) M 2 = 2 Mj (B) M 2 > 2 Mj (C) M 2 < 2 Mj (D) M l < 10 (m n + m p)

(ii) The half-life of 1 3 1 I is 8 days. Given a sample o f 1 3 1 1 at time t = 0, we can assert that: (A) no nucleus will decay before t = 4 days (B) no nucleus will decay before t = 8 days (C) all nuclei will decay before t = 16 days (D) a given nucleus may decay at any time after t = 0.


30 60 90 120 Mass Number of Nuclei

Q.31 Nuclei ofa radioactive element A are being produced at a constant rate a . The element has a decay constant X. At time t = 0, there are N 0 nuclei of the element.

(a) Calculate the number N of nuclei of A at time t . (b) If a=2N0?t, calculate the number of nuclei of A after one halflife of A & also the limiting value ofN as t-*».

[JEE '98] E Y O n 1 Q.32(a) Binding energy per nucleon vs. mass number curve for

nuclei is shown in the figure. W, X, Y and Z are four nuclei indicated on the curve. The process that would release energy is (A) Y —> 2Z (B) W —> X + Z ( C ) W - » 2Y (D) X — Y + Z

(b) Order of magnitude of density of Uranium nucleus is, [m p = 1.67 x 10~27 kg] (A) 10 2 0 kg/m3 (B) 10 1 7kg/m 3 (C) 10 1 4kg/m 3 (D) 10 n kg/m 3

(c) 2 2 Ne nucleus, after absorbing energy, decays into two a-particles and an unknown nucleus. The unknown nucleus is (A) nitrogen (B) carbon (C) boron (D) oxygen

(d) Which of the following is a correct statement? (A) Beta rays are same as cathode rays (B) Gamma rays are high energy neutrons. (C) Alpha particles are singly ionized helium atoms (D) Protons and neutrons have exactly the same mass (E) None

(e) The half-life period of a radioactive element X is same as the mean-life time of another radioactive element Y. Initially both of them have the same number of atoms. Then (A) X & Y have the same decay rate initially (B) X & Y decay at the same rate always (C) Y will decay at a faster rate than X (D) X will decay at a faster rate than Y [JEE'99]

Q.33 Two radioactive materials Xj and X 2 have decay constants 10X. and X respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of Xj to that of Xj will be 1/e after a time (A) 1/(10X) (B) 1/(1 IX) (C) 11/(1 OA,) (D)1/(9A) [JEE'2000 (Scr)]

Q.34 The electron emitted in beta radiation originates from [JEE'2001(Scr)] (A) inner orbits of atoms (B) free electrons existing in nuclei (C) decay of a neutron in a nucleus (D) photon escaping from the nucleus

Q.35 The half-life o f 2 1 5 A t is 100 ps. The time taken for the radioactivity of a sample o f 2 1 5 At to decay to

Q.36

Q.37

Q.38

Q.39

1/16 th of its initial value is (A) 400 ps ( B ) 6.3 ps (C) 40 ps Which of the following processes represents a gamma - decay? (A) A X Z + y > A X Z _ ! + a + b (C) A x z — > A x z + / ( D ) A X 2

( B ) A X z + i n 0

v z + e _ !

[JEE 2002 (Scr)] (D) 300 ps

[JEE 2002 (Scr)] - * A - 3 X 7 „ + C - > A X Z - 2

i + 8 [JEE 2003 (Scr)]

(D) v oc 1/m2

The volume and mass of a nucleus are related as (A) v qc m (B) v cc 1/m (C) v cc m 2

The nucleus of element X (A= 220) undergoes a-decay. If Q-value of the reaction is 5.5 MeV, then the kinetic energy of a-particle is : [JEE 2003 (Scr)] (A) 5.4MeV (B)10.8MeV (C)2.7MeV (D)None A radioactive sample emits n P-particles in 2 sec. In next 2 sec it emits 0.75 n P-particles, what is the mean life ofthe sample? [JEE 2003 ]


Q.40 The wavelength of K x X-ray of an element having atomic number z = 11 is X. The wavelength of K a

X-ray of another element of atomic number z' is 4A. Then z' is (A) 11 (B) 44 (C) 6 (D) 4 [JEE 2005 (Scr)]

Q. 41 A photon of 10.2 eV energy collides with a hydrogen atom in ground state inelastically. After few microseconds one more photon of energy 15 eV collides with the same hydrogen atomThen what can be detected by a suitable detector. (A) one photon of 10.2 eV and an electron of energy 1.4 eV (B) 2 photons of energy 10.2 eV (C) 2 photons of energy 3.4 eV (D) 1 photon of 3.4 eVand one electron of 1.4 eV [JEE 2005 (Scr)]

Q. 42 Helium nuclie combines to form an oxygen nucleus. The binding energy per nucleon of oxygen nucleus is if m 0 = 15.834 amu and m H e = 4,0026 amu (A) 10.24 MeV (B)0MeV (C) 5.24 MeV (D) 4 MeV

[JEE1 2005 (Scr)] Q. 43 The potential energy of a particle of mass m is given by

V(x)= E„ 0 < x < 1 x >1

Xl and X

2 are the de-Broglie wavelengths of the particle, when 0 < x < 1 and x > 1 respectively. If the

total energy of particle is 2E 0, find Xl/ X

2. [JEE 2005]

Q. 44 Highly energetic electrons are bombarded on a target of an element containing 3 0 neutrons. The ratio of radii of nucleus to that of helium nucleus is (14) 1 / 3. Find

(a) atomic number of the nucleus (b) the frequency of K a line ofthe X-ray produced. (R= l . lx 1 0 7 m _ 1 andc = 3 x 10 8m/s)

[JEE 2005] Q.45 Given a sample of Radium-226 having half-life of 4 days. Find the probability, a nucleus disintegrates

within 2 half lives. (A) 1 (B) 1/2 (C) 3/4 (D) 1/4 [JEE 2006]

metal 2 metal 3 Q .46 The graph between 1IX and stopping potential (V) ofthree metals

having work functions (j , (J>2 and <j)3 in an experiment of photo-electric effect is plotted as shown in the figure. Which of the following statement(s) is/are correct? [Here X is the wavelength of the incident ray]. (A) Ratio of work functions : <j)2 : <t>3 = 1 :2 : 4 (B) Ratio of work functions ()>, : <j)2 : (j)3 = 4 : 2 : 1 (C) tan 9 is directly proportional to hc/e, where h is Planck's constant and c is the speed of light (D) The violet colour light can eject photoelectrons from metals 2 and 3. [JEE 2006]

Q. 47 In hydrogen-like atom (z = 11), n t h line of Lyman series has wavelength X equal to the de-Broglie's wavelength of electron in the level from which it originated. What is the value of n? [JEE 2006]

0.001 0.002 0.004 l/X

Q. 4 8 Match the following Columns Column 1

(A) Nuclear fusion (B) Nuclear fission (C) (3-decay (D) Exothermic nuclear reaction

[JEE 2006] Column 2

(P) Converts some matter into energy (Q) Generally occurs for nuclei with low atomic number (R) Generally occurs for nuclei with higher atomic number (S) Essentially proceeds by weak nuclear forces


A N S W E R K E Y EXERCISE # I

Q.l 885 Q.2 (a) 2.25eV, (b) 4.2eV, (c)2.0 eV, 0.5 eV Q.3 (a) 0.6 volt, (b)2.0mA Q.4 when the potential is steady, photo electric emission just stop when hu = (3 + l)eV = 4.0 eV

5.76 x 1 0 _ n A Q.6 15/8 V Q.7 487.06nm Q.8 4.26m/s, 13.2eV X { X

2

Q.5 Q.9 7 :36 Q.10 22.8 nm Q.l l

Q.13 1.257 x 1CT23 Am 2 Q.14 2.48 xlO" 1 2 m Q.15

A i + X2

5 10 20

16' 8071

Q.12 18/(5R)

Q.16 2eV, 6.53 x lO- 3 4J-s

Q.17 5 Q , i 9 " z = 3,n = 7 Q.23 ( T 1 / 2 = 10.8 sec)

Q.18 (i) 5, 16.5 eV, 36.4A, 340 eV, - 6 8 0 eV, — 1 . 0 6 x l 0 ~ n m 2tc Q.20 54.4 eV Q.21 n = 3 , 3 : 1 Q.22 23.6 MeV Q.24 (i) ?9°K —•> Ar + + 1 e° + v (ii) 4.2 x 109 years

Q.25 t = v / n 2 y

Q.26 8/3xlO 1 8 sec Q.27 1.14 x 10 1 8 sec EXERCISE # II

Q.2 4.8 x 10 1 6, 4.0 cm Q.5 (i) 4125A, (ii) 13.2 pA

Q.28 -h/eEt 2

Q.3 1.99 eV, 0.760 V 3 8 I R h Q.l 8IhR/3C 1 5 C

Q.4 1.1 x i o 1 2

Q.6 (i) 1,33 x 10 1 6 photons/m 2 -s ; 0.096 pA(ii) 2.956 x io 1 5 photons/m2s ; 0.0213 pA(iii) 1.06 volt Q.7 (i) 5/16 photon/sec, (ii) 5/1600'electrons/sec

Q.9 X =

Q.8 XA

yjx{2+x 2 Q.12 11.24 eV

1 r 2

Q15 ( i ) -

deutron ""neutron ^ ' ^ P ^

Q.10 3.1 x 10 6m/s Q. l l (i) 2; (ii) 23.04 xlO- ! 9 J; (iii) 4 1 , 4 - > 3 Q.13 6.8 eV, 5 x l 0 1 5 H z Q.14 489.6 eV, 25.28A

1 e z

87i80 r (ii) ro { „ 2 \ 1 / 3 , 3Cr e t 1 ~

v

100 'o J

, (iii) 10" 1 0 x sec 81 Q. 16 (i) 1.875 x i o 4 V, (ii) 2.7 x 10" 1 5 J, (iii) 0.737 A, (iv) 2.67 x 10" 1 5 J Q.17 6.04 x io 9 yrs Q.18 4.87MeV Q.19 3 . 3 x l 0 - 6 g Q.20 1.7 x i o 1 0 years Q.21 7.01366 amu Q.22 (a) 4 MeV, 17.6 (b) 7.2 MeV (c) 0.384 % Q.23 5196 yrs Q.25 Energy of neutron = 19.768 MeV; Energy ofBeryllium= 5.0007 MeV;

Angle of recoil = tan"1 (1.034) or 46°

0.2Er Q.26 v = uXt Q.27 AT

mS


EXERCISE # III Q.l (i) Allowed values of energy of neutron = 6.36 eV and 0.312 eV; Allowed values of energy of He atom

= 17.84 eV and 16.328 eV, (ii) 18.23 x 10 1 5 Hz, 9.846 x 10 1 5 Hz, 11.6 x 10 1 5 Hz Q.2 n = 6, Z = 3 Q.3 B, C Q.4 (a) 105 s"1 ; (b) 286.18 ; (d) 111 s

he ehB Q.5 D Q.6 (i) KE = 3.4 eV, (ii) A = 6.66 A Q.7 (i) (ii) Q.8 0.61 A Q.9 (i)D, (ii) KE= 151 eV, d l e a s t =0.5 A

47tm 871m Q Q Q Q Q

10 (i) C (ii) A, D Q.l l C 12 during combination = 3.365 eV; after combination = 3 .88 eV (5 -> 3) & 2.63 eV (4 -> 3) 13 (a)C, (b)A 14 (a) n = 2, z = 4; GS.E. - 217.6 eV; Min. energy =10.58 eV; (b) 6.25x 10 1 9 per sec, 0, 5 eV 15 A

Q.19 A

Q.16 B

Q.20 z = 42

Q.17 3,4052.3 nm Q.18 5xl07,2000N./C, 23 eV 1

8|IA

Q.21 - 2 V

1=2x10- 5 W / m 2

1=10 - 5 W / m 2

V P

Q.22 C

Q.26 C

Q.23 6 litre Q.24 ( i )B,( i i )A Q.25 A, D

Q.27 (i) t = 10 sec., t = 14.43 s (ii) 40 seconds ^ v 1/2 ' means v y

Q.28 Fusion, 24 Q.29 (a) B, (b) (i) - A, (ii) - E, (iii) - F , (iv) - C, (c) = 33.298 pW

1 3N Q.30 (i) C, D (ii) D Q.31 (a) N = — [a (1 - e~ l t

)+ X N 0e~X t] (b) — X 2 0 2 N

Q.32 (a) C ;(b) B ;(c) B ; ( d ) E ; (e) C Q.33 D

Q.34 C Q.35 A Q.36 C Q.37 A Q.38 A Q.39 1 .75n-N 0 ( l e" 4 ^, 6.95 sec, 2 Q.40 C

In

Q.41 A Q.42 A Q.43 V2

Q.45 C Q.46 A,C Q.47 n = 24

Q 48 (A) P, Q; (B) P, R; (C) S, P; (D) P, Q, R

Q .44 v = 1.546 x 10 1 8 Hz


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