q. what is the de broglie wavelength of an electron that has a kinetic energy of 100 ev? after an...

Q. What is the de Broglie wavelength of an electron that has a kinetic energy of 100 eV?

After an electron is accelerated in 100 V potential difference, its kinetic energy is 100 eV.eV unit has to be converted into SI unit, Joule.

1 eV = 1.6 x 10-19 J

Ek = (1/2)mov2 = 1.6 x 10-17 J

v2 = 2Ek/mo = 2(1.6 x 10-17 J)/(9.1 x 10-31 kg) = 3.52 x 1013 m2/s2

v = 5.93 x 106 m/s low speed: no need to use relativistic

= h/p = h/mov = (6.6 x 10-34 Js)/(9.1 x 10-31 kg x 5.93 x 106 m/s) = 1.23 x 10-10 m = 0.123 nm

The Atomic Nucleus

Composed of nucleons: proton (+e) and neutrons (neutral)mp = 1.673 x 10-27 kg = 938.28 MeVmn = 1.675 x 10-27 kg = 939.4 MeVme = 9.1 x 10-31 kg = 0.511 MeV

Positively charged (# of protons = # of electrons)Heavy object: most of the atomic mass is concentrated in the nucleusSize ≈ 10-14 m = 10 femtometer (10-15 = femto)

Considering the size of an atom ≈ 10-10 m, an atom is mostlyempty.

The force binding nucleons together should overcome Coulomb repulsion!Nuclear force is very strong and attractive.

Each element has different # of protons periodic table is arranged by the # of protons.

E = mc2

atomic number: Z

Z= # of electrons: chemical property

Missing information about the # of neutrons?

8 neutrons

146 neutrons

“I began to look about and write down the elements with their atomic weights and typical properties, analogous elements and like atomic weights on separate cards, and this soon convinced me that the properties of elements are in periodic dependence upon their atomic weights.”

--Principles of Chemistry, 1905, Vol. II

Dmitri Ivanovich Mendeleev (1834-1907)

atomic mass number (A): total # of protons and neutronsA = Z + N (integer)

XA

Zelement

ElementElement SymbolSymbol ZZ NN Mass #Mass #

HydrogenHydrogen 11 00 11HeliumHelium 22 22 44LithiumLithium 33 44 77UraniumUranium 9292 146146 238238

H11He42

U23892

Li73

Approximate radius, R, for the nucleusR = (1.2 x 10-15)A1/3 m

The actual mass of atom or nucleus is expressed in atomic mass units (U).

1 u = 1.6607 x 10-27 kg= 931 MeV

Exactly equal to one-twelfth of the mass of the most abundant form of the carbon atom

mp = 1.673 x 10-27 kg = 1.007276 umn = 1.675 x 10-27 kg = 1.008665 ume = 9.1 x 10-31 kg = 0.00055 u

The average atomic mass of mercury (Hg) is 200.59 u. What is the average nuclear mass for Hg atom?

Z = 80 for Hg there are 80 electrons.

Mass of electrons in Hg atom = 80 x 0.00055 u = 0.044 u

Nuclear mass = atomic mass – electron mass = 200.59 u – 0.044 u = 200.55 u

include everything (p, n, and e)

Isotopes

Atoms that have the same atomic number (Z) but different mass numbers (A).

XA

Z

Li7

3Li

6

3

Natural abundance: 92% 8%

Co58

27Co

60

27

Helium Nucleus

He4

2

atomic mass = 4.002602 u2 electrons: electron mass = 2 x 0.00055 u

= 0.0011 unucleus mass = 4.002602 u – 0.0011 u

= 4.001502 u

We know He nucleus is composed of 2 protons and 2 neutrons:

2 proton mass = 2 x 1.007276 u2 neutron mass = 2 x 1.008665 utotal mass = 4.031882 u > He nucleus mass

m = 4.031882 u – 4.001502 u = 0.030376 u

All nuclei have a mass that is smaller than the sum of the masses of its separated nucleons. This difference in mass is called the mass defect.

E = mc2E = mc2

binding energy of the nucleons in the nucleus

m for He = 0.030376 u = 0.030376 x (1.66 x 10-27 kg) = 5.0 x 10-29 kg

E = mc2 = (5.0 x 10-29 kg)(3 x 108 m/s)2

= 4.5 x 10-12 J = 28 MeV

1 u = 1.6607 x 10-27 kg = 931 MeV

= 0.030376 x 931 MeV= 28.2 MeV

binding energy per nucleon in He = 7 MeV

np

He nucleus

28 MeV

Ex. 31.4 How much energy is released as 1 kg of neutrons and 1 kg of protons are changed into 2 kg of helium 4 nuclei?

# of He nuclei in 2 kg = 2 kg/(4 x 1.66 x 10-27 kg) = 3.0 x 1026

28 MeV is released per nucleus:total energy released = 28 x 3.0 x 1026 MeV

= 8.4 x 1027 MeV = 1.5 x 1015 J

New York city needs 1010 W of electricity. This amount can run NY city for 2 days!!

Radioactivity

Sometimes particles or photons are emitted from the nuclei of atoms: unstable nuclei

radioactive

unstable nuclei stable nuclei

all naturally occurring elements with Z > 83

Three major forms of radioactive emission:

Alpha particle (): nucleus of a He atom

Beta particles (): beta minus particle (electron)

beta plus particle (positron)

Gamma rays (): high energy photons, short wavelength x-ray

420101

XA

ZX

A

Z+

XA

ZX

A-4

Z-242+

XA

ZX

A

Z+1+ 01

A and Z are conserved in nuclear reaction!!

T1/2: half-life

N(t) = Noe-pt

# of unstable nuclei at time t

Initial # of unstable nuclei at time t = 0

At T1/2, N(T1/2) = (0.5)No

692.02ln

2

1lnln

2

1)(

2/1

2/1

2/1

2/1

pT

e

eN

TN

pT

pT

o

If you know T1/2, you can get p from this equation. Then, at any time you can calculate # of unstable nuclei. Or, with the knowledge of # of unstable nuclei, we can calculate how much time has passed. Carbon dating

decay constant

Carbon Dating

By measuring the ratio of 14C isotope to 12C in a biological sampleone can calculate the age of the object from which the sample came with the knowledge of the initial ratio when the biological activity ceased.

should be dead!

half-life: 5730 yrs?

bbc.co.uk

A mummy found in Egypt

147N + 1

0n 146C + ? 1

1p

Ratio of 14C to 12C?

Before 1900 (atomic bomb testing)1.5 x 10-12

146C 14

7N + ? 0-1

beta decay

bbc.co.uk

A mummy found in Egypt

Measured the ratio of 14C to 12Cr(t) = 1.05 x 10-12

ro = 1.5 x 10-12

T1/2 = 5730 yrs

Let’s calculate decay const, pp = 0.693/T1/2

= 0.693/5730= 1.21 x 10-4 (yr-1)

Total # of 12C = N12

# of 14C = N14 = r(t)N12

r(t)N12 = roN12e-pt

r(T)/ro = (1.05/1.5) = e-pT

ln(0.7) = -pTT = -ln(0.7)/(1.21 x 10-4) = 2848 yr

Ex. 31.10 Cobalt-60 has a half-life of 5.25 yrs (1.66 x 108 s). Given 1 mg of the substance, find (a) the number of atoms in the sample, (b) the decay constant, (c) the time taken for 0.01 mg to decay.

mass of Co-60 = 59.93381 u = 60 u= 60 x 1.66 x 10-27 kg= 1.0 x 10-25 kg

No = (1 x 10-6 kg)/(1 x 10-25 kg) = 1 x 1019 atoms

p = 0.693/T1/2 = 0.693/(1.66 x 108 s) = 4.2 x 10-9 s-1

How long does it take to reach N/No = 0.99?ln(N/No) = -pt

ln(0.99) = -(4.2 x 10-9)tt = 2.4 x 106 s about a month

1 yr = x 107 s

Which of the following nuclear reaction is(are) impossible?Which of the following nuclear reaction is(are) impossible?

(a) (a) 2312319191Pa Pa + + 227227

8989AcAc (b) (b) 1414

66C C 141477N + N + +1+1

(c) (c) 2402409292U U -1-1 + + 240240

9393NpNp

45

20% 20% 20%20%20%

1.1. (a)(a)

2.2. (b)(b)

3.3. (c)(c)

4.4. AllAll

5.5. NoneNone

Nuclear Fission

In a chemical reaction, changes in atoms are in their electron configuration. However, in a nuclear reaction, the configuration of nucleus changes by emitting or absorbing typically high energy photons, nucleons, alpha particles, and/or light charged particles. In this process, charge, nucleons, and mass-energy are conserved.

Nuclear fission: Unstable heavy nucleus multiple intermediate mass nuclei

+ large energy

U235

92

n

stable isotopeT1/2 ≈ 109 yrs

U236

92

unstable

Kr95

36

Ba138

56

n

n

n

200 MeV per fission

In 1938, Otto Hahn, Lise Meitner, and Fritz Strassmann discovered:

235U 236U 92Kr141Ba

n

Chain Reaction

Through the release of atomic energy, our generation has brought into the world the most revolutionary force since prehistoric man's discovery of fire. This basic force of the universe cannot be fitted into the outmoded concept of narrow nationalisms. For there is no secret and there is no defense; there is no possibility of control except through the aroused understanding and insistence of the peoples of the world. We scientists recognise our inescapable responsibility to carry to our fellow citizens an understanding of atomic energy and its implication for society. In this lies our only security and our only hope - we believe that an informed citizenry will act for life and not for death.

A. Einstein, 1947

"When you sit with a nice girl for two hours, it seems like two minutes. When you sit on a hot stove for two minutes, it seems like two hours that's relativity."

"Gravitation is not responsible for people falling in love."