CONCEPT MAPS

Unit 1: Electrostatics(08 marks)

Revise:SI units and dimensions of electric charge, field, dipole moment, flux and charge densities, potential, capacitance and polarisation. Drawing field lines and EPS for dipole, two charge and single charge system.

Vector form of Coulombs Law. Gauss Theorem, electric dipole, electric field lines and equipotential surface. capacitor, Van de Graff Generator

Remember:Charge is scalar but the electric field created by it is a vector, whereas the potential is again a scalar. Electric flux is a scalar. A dipole experiences no force but pure torque in uniform electric field whereas it does experience a force and torque both in non-uniform field. Gausss Law is valid only for closed surfaces. Three types of charge densities viz linear, surface and volume are different physical quantities having different unit and dimensions. Along a field line, potential decreases at the fastest rate. The dipole moment per unit volume is called polarisation and is a vector. Whether its a solid or a hollow conducting sphere, all free charges reside on its surface. Dielectric constant is also called relative permittivity and is dimensionless, unitless.

Unit 2:Current electricity(07 marks)

Revise :SI units and dimensions of mobility, resistance, resistivity,conductivity, current density and emf. Ohms Law , drift velocity, colour coding. Parallel/ series combination of cells. Potentiometer. Numericals on finding equivalent resistance/current using Kirchoffs laws

Remember:Current is scalar as it does not follow laws of vector addition but current density is vector. Kirchoffs junction/ loop law is charge/ energy conservation laws. If the Galvanometer and cell are interchanged in balanced Wheatstone bridge, the balance does not get affected. For a steady current along a tapering conductor, current remains constant but current density, drift speed and electric field varies inversely as area of cross-section. Ohms law is not universally applicable such as vacuum diode, semiconductor diode.

Unit 3: Magnetic effects of current and magnetism:(08 marks)

Revise :SI units and dimensions of permeability, relative permeability, magnetic moment, field, flux, intensity, susceptibility, torsional constant and their nature as vector or scalars. Magnetic field lines. Biot-Savart and Amperes law, solenoid, toroid, MCG, Cyclotron, para, dia and ferro magnetism, permanent and electromagnets. Numericals on ammeter and voltmeters

Remember:Parallel currents attract and anti parallel currents repel. Amperes law can be derived from Biot- Savarts law. MCG has two sensitivities voltage and current as deflection per unit voltage/ current, respectively. Angle of dip is also called inclination, its value at poles and at equator are 90 degrees and 0 degree, respectively.

Superconductors are perfect diamagnets. T(tesla) is SI unit for magnetic field, the other being G(gauss,non-SI),1 T is equal to 10,000 gauss.

Diamagnetism is universal - it is present in all materials.

Unit 4: EMI and AC(08 marks )Revise :SI unit and dimensions of self and mutual inductance, capacitive and inductive reactance, impedance, Q-factor, power factor. Faradays/ Lenzs law, eddy current, motional emf, self/ mutual inductance, AC generator, transformer

Remember:Lenzs law is consequence of energy conservation. Eddy current has merits and demerits. AC is scalar but follows phasor treatment as it is periodically varying. At resonance power factor is 1, hence maximum power is dissipated. A transformer works in AC but not in DC. The power consumed in an AC circuit is never negative. Rated values of ac devices for current and voltages are rms whereas for power it is average. Higher the Q-factor sharper the resonance, smaller the bandwidth and better the selectivity

Unit 5: Electromagnetic waves(03 marks)Revise :Properties and frequencies, Ampere-Maxwell law, displacement current, drawing of EMW. Numericals on finding frequency, speed etc from given equation.

Remember :An oscillating charge produces EMW of the frequency of oscillation. IR waves are also called heat waves as they produce heating. The AM (amplitude modulated) band is from 530 kHz to 1710 kHz. TV waves range from 54 MHz to 890 MHz. The FM (frequency modulated) radio band extends from 88 MHz to 108 MHz. TV remote uses IR waves. LASIK and water purification uses UV rays.

Unit 6: Optics(14 marks)Revise :Lens and Lens makers formula, magnifying and resolving power, limit of resolution, Hygens principle and polarisation, YDSE. Numericals on image location and its nature for lens-mirror combinations

Remember:Resolving power is inverse of limit of resolution. Unpolarised light after passing through a polaroid gets linearly polarised with half the intensity for any orientation of the polaroid. Diffraction, interference and polarisation prove the wave nature of light. Polarisation proves the transverse nature of light. Compound microscope has eyepiece of larger aperture and objective smaller vice versa in a telescope. Reflecting telescope removes chromatic and spherical aberration fairly. If the source of light is white in YDSE the central fringe is white and others are coloured in sequence from nearest red to the farthest blue.

Unit 7: Dual nature of matter and radiation(04 marks)Revise :Einsteins photoelectric equation and all the graphs in the NCERT book. Davisson-Germer experiment. Numericals based on de Broglies and photoelectric equations.Remember :de Broglie equation relates particle to wave. Wave nature of electrons are used in electron microscope. Photoelectric effect was explained using photon picture of light.

Atom & nucleus1. Discovery of nucleus In 1897 J.J. Thomson discovered the electron in the rays emitted from the cathode of discharge tube filled with gas at low temperatures. Again 1910 Thomson suggested a model for describing atom , known as 'Thomson's atomic model' which suggests that atom consists of positively charged sphere of radius 10-8cm in which electrons were supposed to be embedded. Thomson atomic model failed as it could not give convincing explanation for several phenomenon such as, spectrum of atoms, alpha particle scattering and many more. In 1909 Gieger and Marsden employed -particles (Helium ion) as projectile to bombard thin metallic foil. According to Thomson atomic model since all positive charge of atom was neutralized by the negatively charged electrons, there would be rare event for an -particle to suffer a very large deflection , as expected force of repulsion would not be very strong. Surprisingly experiments of Gieger and Marsden showed large deflections of alpha particles that were many orders of magnitude and more common then expected. This result of Gieger and Marsden -particle scattering experiment was explained by Sir Rutherford in 1911. Rutherford proposed a new atomic model in which electrons were located at much greater distance from the positive charge. Rutherford proposed that all the positive charge , and nearly all the mass of the atom, was concentrated in an extremely small nucleus. The electrons were supposed to be distributed around the nucleus in a sphere of atomic radius nearly equal to 10-8cm. In explaining this experiment Rutherford made simple assumptions that both the nucleus and -particles (Helium ion) were point electrical charges and the repulsive force between them is given by Coulombs inverse square law at all distances of separation. These assumptions made by Rutherford were not valid if -particle approaches the nucleus to a distance comparable with the diameter of the nucleus. From this experiment there emerged a picture of internal structure of atoms and it also confirmed the existence of the atomic nucleus. Approximate values for size and electrical charge of nucleus were calculated using data of various scattering experiments.

2. Nuclear Composition Atomic nuclei are build up of protons and neutrons. Nucleus of hydrogen atom contains only single proton. Charge on a proton is +1.6x10-19 C and its mass is 1836 times greater then that of electron. Neutrons are uncharged particles and mass of a neutron is slightly greater then that of a proton. Neutrons and protons are jointly called nucleons. Number of protons in nuclei of an element is equal to the number of electrons in neutral atom of that element. All nuclei of a given element does not have equal number of neutrons for example99.9 percent of hydrogen nuclei contains only one proton , some contain one proton and one neutron and a very little fraction contains one proton and two neutrons. Elements that have same number of protons but differ in number of neutrons in their nucleus are called ISOTOPES. Hydrogen isotope deuterium is stable but tritium is radioactive and it decays to changes into an isotope of helium.

In heavy water instead of ordinary hydrogen deuterium combines with oxygen. Symbol for nuclear species follows the pattern AXZ whereX= Chemical symbol of element Z= Atomic number of element or number of protons in the nucleus of that element.A= Mass number of nuclide or number of nucleons in the nucleus. A=Z+N where N is the number of neutrons in the nucleus. In symbolic form (1)hydrogen = 1H1 and Deuterium = 2H1(2)Chlorine isotopes are 35Cl17 and 37Cl17

3. Atomic mass Atomic masses refer to the masses of neutral atoms , not of bare nuclei i.e., an atomic mass always includes the masses of all its electrons. Atomic masses are expressed in mass units (u). One atomic mass unit is defined as one twelfth part of the mass of 12C6 atom. So the mass of 12C6, the most abundant isotope of carbon is 12u. Value of a mass unit is 1u=1.66054x10-27Kg We now calculate the energy equivalent of mass unit. We know that Einsteins Mass-Energy relation is E=mc2here,m = 1.60x10-27 Kg andc = 3x108 m/sthereforeE = (1.60x10-27) x (3x108)2 =1.49x10-10 Jbut 1eV = 1.6 x 10-19 Jtherefore, E = 1.49 x 10-10

1.60 x 10-19

or,E = .931 x 109 eVE = 931 MeVThus 1 amu = 931 MeV Mass of proton is 1.00727663 u which is equal to 1.6725 x 10-27kg or 938.26 MeV. Mass of neutron is 1.0086654 u which is equal to 1.6748 x 10-27kg or 939.55 MeV.

4. Isobars and Isotones Nuclei with same A but different Z are known as Isobars for example 40K19 and 40Ca20 share same mass number 40 but differs in one unit of Z. Although isobaric atoms share same mass number but they differ slightly in their masses. This very slight difference in masses of isobaric atoms is related to difference between energies of two atoms since small mass difference corresponds to considerable amount of difference in energies. Nuclei with same number of neutrons but different number of protons are called Isotones for example 198Hg80 and 198Au79

5. Size of nucleus First estimate of size of nucleus was provided by Rutherford scattering experiment. In Rutherfords scattering experiment incident alpha particles gets deflected by the target nucleus as long as the distance approached by the alpha particles does not exceeds 10-14m and Coulombs law remains consistent. Apart from Rutherfords scattering experiment various other experiments like fast electrons and neutron scattering experiments were performed to determine the nuclear dimensions. Since electrons interact with nucleus only through electric forces so electron scattering experiments gives information on distribution of charge in the nucleus. A neutron interacts with nucleus through nuclear forces so neutron scattering provides information on distribution of nuclear matter. It was found that the volume of a nucleus is directly proportional to the number of nucleons it contains which is its mass number A. If R is the nuclear radius then relationship between R and A is given asR=R0A1/3Where value of R0 1.2 x 10-15 1.2 fm and is known as nuclear radius parameter. Since R3 is proportional to A this implies that density of nucleas ( = m/V) is a constant independent of A for all nuclei. The density of nuclear matter is approximately of the order of !17 Kg/m3 and is very large compared to the density of ordinary matter.

1) Introduction Phenomenon of radioactivity was first discovered by A.H.Bacquerel in 1896 while studying fluorescence and phosphorence of compounds irradiated by visible light these phosphorescent materials glow in dark after being exposed to visible light while conducting experiment on uranium salts, he found that uranium salts has a capability to blacken the photographic plate kept in a dark place wrapped through a paper Subsequent experiments showed that radioactivity is a nuclear phenomenon in which an unstable nucleus under goes a decay process referred as radioactive decay There are three types of radioactivity decays that occur in nature .These are decay , decay and decay. We now define radioactive decay as the process by which unstable atomic nucleus looses energy by emitting ionizing particles or radiations ( , and rays) Radioactive decay of an atomic nucleus is a spontaneous process and can occur without any interaction of other particles outside the atom This process of radioactive decay is random and we can not predict whether a given radioactive atom will emit radiations at a particular instant of time or not Phenomenon of radioactivity is observed in heavy elements like uranium and unstable isotopes like carbon 142) Properties of radioactive decay Radioactive rays ionize the surrounding air and affect photographic plate Radioactive rays acts differently on different biological cells and tissues A beam of radioactive rays from a radium sample into three components in presence of strong magnetic or electric fieldsI.The alpha rays(particles) The alpha particles are nuclei of helium atoms Alpha particles was first identified by Rutherford and Royds in 1909 by spectroscopic method where they found traces of helium in an originally pure sample of Radon gas which is an emitter. Examples of decay are

(A)222Rn864He2+218Po84

(B) 238U924He2+234Th90 rays can be stopped by thin sheet of paper. rays can cause intense ionization in air. Any group of particles emitted from same type of nuclei always have definite energy and definite velocity. Most particles are emitted with velocities between 1.5x107 and 2.2x107. The particles cover a definite distance in a material without any loss of intensity and suddenly in a small distance they are absorbed completely. The distance rays travel within a given material is called their range in that material.II.The beta rays(particles) particles are identical with electrons. They have mass 1 1836 of mass of proton. examples of decay are(A)234Th90 234Pa91+e-

(B) 210Bi83 210Po84+e-

(C) 14C6 14N7+e- Mass number and charge are conserved and the daughter product moves one place up in the periodic table, as loss of negative charge by nucleus implies gain of positive charge. rays cause much less ionization in air , but are 100 times more penetrating then rays. rays can penetrate a aluminum sheet of few mm thickness. A particular active element emits particles with energies varying between zero and a certain maximum. This maximum energy is called end point energy.III. The Gamma rays:- They are part of EM spectrum < X-rays ray photons are more energetic and more penetrating then X-rays photons rages between 1.7X10-8 cm and 4.0X10-6 cm Ionization due to Gamma rays is a photoelectric effect Owing to their large energies ,the Gamma rays photons can dislodge electrons not only from outer orbits( valence orbits on conduction band) of atoms but also from the inner orbits Besides photoelectric effect ,gamma rays loose energy by i) Compton effect ,in which the gamma photon collides with an electron and gets scattered with a shift in wavelength

ii) Pair production ,in which a gamma photon is converted into a pair consisting of an electron and a positron( particle having mass and charge equal to electron but carrying positive change)3) Law of radioactive Decay Radioactivity is a nuclear phenomenon When a nucleus disintegrates by emitting a particle ( and ) or by capturing an electron from the atomic shell( K-shell) ,the process is called radioactive decay. This decay process is spontaneous. Let us take a radioactive sample containing N0 at time t=0 i.e, at the beginning. We wish to calculate the number N of these nuclei left after time t. The number of nuclei of a given radioactive sample disintegrating per sec is called the activity of that sample isdN/dt=rate of decrease of nuclei with time=Activity of sample at time t --(1) Experimentally it is found that the activity at any instant of time t is directly proportional to the number N of parent type nuclei present at that time

Where > 0 is proportionality constant and negative sign indicates that N decreases as t increases From equation (2) we get

i.e. , is fractional change in N per sec=> is not merely a proportionality constant ,but it gives us the probability of decay per unit interval of time Hence is called the probability constant or decay constant or disintegration constant dN is the no of parent nuclei that decay between t and t+dt and we have taken N as continuous variable From (2)

N0=No of radioactive nuclei at t=0 From (4) we see that law of radioactive decay is exponential in character

From figure it can be noted that only half the amount of radon present initially after 3.83 days and 1/4 after 7.66 days and so on Plot shows that in a fixed time interval a fixed fraction of the amount of radioactive substance at the beginning of interval decays This faction is independent of the amount of radioactive substance and depends only on the interval of the time The decay constant is a characteristics of radioactive substance and it depends in no way on the amount of the substance presenta) Half Life Time interval during which half of a given sample of radioactive substance decays is called its half life. It is denoted by T

b) Mean Life Individual radio atomic atoms may have life spans between zero and infinity Average or mean life is defined as=Total life time of all nuclei in a given sample/Total no of nuclei in that sample --(6)

From curve one can see that each of dN number of radioactive nuclei has lived a life of t sec i.e. the total life span of a dN nuclei is (dN.t) sec . Therefore equation (6) can be written as

4) Unit of activity The most commonly used unit is the curie Curie was originally based on the rate of decay of a gram of radium There are 3.7X1010 disintegrations per sec per gram of radium .This no is taken as a standard=> One curie=3.7X1010 disintegrations per sec One curie of activity is very strong source of radiation=> 1 milli curie=1mCi=10-3 Ci1 microcurie=1Ci=10-6 Ci Another unit of activity is Rutherford1rd=106 dis/sec Activity |dN/dt|=N=.693N/T=> A very short lived substance gives rise to large activity ,even it is present in minute quantities The SI unit of radioactivity recently proposed is Becquerel (Bq) which is defined as activity done to one disintegration per sec hence1ci=3.7X1010 bq=37G bq 5) Alpha decay: Nucleus before the decay is called parent nucleus and after the decay is called daughter nucleus In Alpha decay, the parent nucleus AXZ emits an particle (=4He2) leaving behind a daughter nucleus of four mass unit less and two charge units less i.e. A-4XZ-2

decay shift the element two places to the left in the periodic tables of elements ex

All nuclides of A >= 210 and Z > 83 tends to decay by emission 209Bi is the heaviest stable nuclide in nature decay in heavy nucleus occur because a too heavy nucleus becomes unstable due to coulomb repulsion and by emitting an particle the nucleus decrease its A and Z to moves towards stability Now the rest mass energy of parent nucleus AXZ is greater then the sum of rest mass energies of A-4XZ-2 and 4He2 The difference between the rest mass energies of initial constituents and final products is called Q-value of the process For decay process ,Q value isQ=[mp -(md+m)]c2where mp -> Mass of parent nucleus ZAXmd -> Mass of parent nucleus Z-2A-4Xm -> Mass of parent nucleus 24He6) Decay There are two types of decay , - and + In decay an nucleus decay spontaneously emitting an electron or positron Under - decay one of the neutrons in the parent nucleus gets transformed into a proton and in the process an electron and an antineutrino are emittedn-> p+e-+- The daughter nucleus thus formed in - decay would be an element one place to the right of the parent in the periodic table of elements Examples of - decay

- is common over entire range of nuclides and amongst the naturally occurring heavy radioactive nuclides and in fission products In + decay one the protons of the parent nucleus gets transformed into a neutron emitting a positron and neutrinop->n+e++ In + decay the daughter nucleus would be one place to the left of parent nuclei in the periodic table Examples of + decay

In both + and - symbol - and represents antineutrino and neutrino Both antineutrino (-) and neutrino() are charge less and nearly less particles and interact very weakly with matter which make their detection very difficult In these decay( + and -) mass number A of nucleus remain same after the decay 7) Decay After alpha or beta decay processes it is common to find the daughter nucleus to be in an excited state Just like atoms ,nucleus also have energy levels So an nucleus in excited state can make transitions from higher energy levels to lower one by the emission of electro magnetic radiation The energy difference in allowed energy levels of a nucleus are of the order of Mev and the photons emitted by nuclei have energies of the order of Mev and are called rays As an example, decay of 60Co27 nucleus gets transformed into 60Ni28 nucleus in excited state which then de -excites to its ground state by successive emission of 1.17 Mev and 1.33 Mev gamma rays as shown in energy level diagram,

IMPORTANT FIVE MARKS QUESTIONS1. Derive an expression for the Electric field at a point on the (i) axial line and (ii) equatorial line of an electric dipole2. Describe the principle construction and working of Van de Graff Generator.3. State Gauss theorem and apply it to find the electric field at a point due to 1. A point charge2. A line of charge3. A plane sheet of charge4. A charged spherical conducting shell4. Derive expression for the potential energy of a system of point charges.5. Derive expression for the torque on a dipole in a uniform electric field.6. Derive expression for the work done in turning a dipole in a uniform electric field.7. Derive an expression for the potential energy of a dipole in a uniform electric field.8. Explain the principle of a parallel plate capacitor9. Derive an expression for the capacitance of a parallel plate capacitor.10. Derive an expression for the effective capacitance when three capacitors are connected in (i) series (ii) parallel11. Derive an expression for the energy stored in a parallel plate capacitor.12. Derive an expression for the loss of energy when two conductors at different potentials are brought into electrical contact. Account for this energy.13. Derive and expression for the energy density of a parallel plate capacitor.14. Derive I = nAeVd15. Define drift velocity and derive an expression for it.16. Deduce Ohms law from elementary concepts.17. State Biot Savarts Law and apply it to find the magnetic field at a point due to long straight conductor carrying current18. State Amperes circuital theorem and apply it to find the magnetic field inside a (i) solenoid (ii) toroid19. State the Principle of a potentiometer and Explain how is it used (i) to determine the internal resistance of a primary cell (ii) to compare the emfs of two primary cells20. State Kirchhoffs laws and apply it to derive Wheatstones bridge principle.21. Explain how will you use a metre bridge to find the resistance of a given resistor wire?22. Describe the elements of earths magnetic field.23. Compare the properties of para dia and ferromagnetic substances.24. Derive an expression for the effective resistance when three resistors are connected in (i) series (ii) parallel25. Describe the principle construction and working of CYCLOTRON. Derive an expression for cyclotron frequency. Why electrons cannot be accelerated in a cyclotron?26. Derive an expression for the force between two straight long parallel conductors carrying constant current and hence define one ampere.27. Describe the principle construction and working of Moving Coil Galvanometer.28. Derive an expression for the torque on a current carrying loop kept in a uniform magnetic field29. Explain how will you convert a galvanometer into (i) an ammeter (ii) a voltmeter30. Define motional emf and derive an expression for it.31. What are eddy currents? Explain its applications32. What is self induction and self inductance? Derive an expression for the self inductance of a long solenoid carrying current33. Define mutual induction and mutual inductance. Derive an expression for the mutual inductance of a pair of solenoids. What are the factors affecting the mutual inductance of a pair of solenoids?34. Derive an expression for the average value of ac for a half cycle.35. Derive an expression for the RMS value of ac36. Explain the principle and construction of a transformer and the various losses in a transformer.37. Derive an expression for impedance of a series LCR circuit. Define resonance is series LCR circuit and derive an expression for resonant frequency.38. Derive an expression for average power in an AC circuit. Define power factor and show that the average power consumed in a pure inductor or a pure capacitor is zero.39. Define Q factor of resonance. Derive an expression for Q factor.40. Derive lens makers formula41. Derive mirror formula42. Derive a relation connecting object distance and image distance when a point object kept in from of a convex refracting surface forms a real image inside the denser medium. (Also practice other similar cases for real images and virtual images as well as for convex interface and concave interface)43. Derive an expression relating angle of prism, angle of incidence, angle of emergence and angle of deviation when light is refracted by a prism44. Derive n = sin (A+D)/2 / sin (A/2) for refraction through a prism.45. Derive an expression for the effective focal length of the combination of two lenses in contacTwo circular coils X and Y having radii R and respectively are placed in horizontal plane with their centers coinciding with each other. Coil X has a current I flowing through it in the clockwise sense. What must be the current in coil Y to make the total magnetic field at the common centre of the two coils, zero?With the same currents flowing in the two coils, if the coil Y is now lifted vertically upwards through a distance R, what would be the net magnetic field at the centre of coil Y?A straight thick long wire of uniform cross section of radius a is carrying a steady current I. Use Amperes circuital law to obtain a relation showing the variation of the magnetic field (Br) inside and outside the wire with distance r, ( ) and ( ) of the field point from the centre of its cross section. Plot a graph showing the nature of this variation.Calculate the ratio of magnetic field at a point above the surface of the wire to that at a point below its surface. What is the maximum value of the field of this wire? 5State the principle which helps us to determine the shape of the wavefront at a later time from its given shape at any time. Apply this principle to:(i) Show that a spherical/ plane wavefront continues to propagate forward as a spherical/plane wave front.(ii) Derive Snells law of refraction by drawing the refracted wavefront corresponding to a plane wavefront incident on the boundary separating a rarer medium from a denser medium.