Nuclear Chemistry

The nuclei of some unstable isotopes change by releasing energy and particles, collectively known as radiation

Spontaneous nuclear reactions - five kinds:

1) Emission of -particles: 42He (helium nucleus)

e.g. 23892U 234

90Th + 42He

In air, -particles travel several cm.

In Al, -particles travel 10-3mm.

2. Emission of -particles: 0–1e (= electron)

e.g. 13153I 131

54Xe + 0–1e

-emission converts a neutron to a proton:

10n 1

1p + 1–1e

In air, -particles travel 10m.In Al, -particles travel 0.5mm.

3. Emission of -rays: 00

-ray emission changes neither atomic number nor mass.

In Al, -particles travel 5-10 cm.

4) Emission of positrons (= anti-electron, or +-particle): 0

+1e

e.g. 116C 11

5B + 01e

Positron emission converts a proton to a neutron:

11p 1

0n + 01e

Positrons have a short lifetime because they recombine with electrons and annihilate:

01e + 0

–1e 2 00

5) Electron Capture: an electron from the orbitals near the nucleus can be captured:

e.g. 8137Rb + 0

–1e 8136Kr

Electron capture converts a proton to a neutron:

11p + 0

–1e 10n

Fill in the blanks 239

94Pu 42He + ?

23491Pa 234

92U + ?

• 11p

• 0–1e

• 10n

• 42He

19277Ir + ? 192

76Os

189F 18

8O + ?

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Because the mechanism is unimolecular, nuclear decay is always a first order process.

Decay Rate = -dN/dt = kN

where: k is a constant, N is the number of decaying nuclei.

Integrated rate law:

ln[N(t)/N0] = -kt

N(t) = N0e-kt

where N0 is the number of radioactive nuclei at t=0.

NUCLEAR DECAY KINETICS

Half-Life: the time required for half of a radioactive sample to decay.

N(t1/2) = N0/2

ln(N/N0) = -kt

k = 0.693/t1/2; t1/2 = 0.693/k

Examples:

Isotope t1/2 Decay

23892U 4.5x109 yr

23592U 7.1x108 yr

146C 5.7x103 yr

Half-Life

Strontium-90, which is a fission product of uranium, has a half-life of 28 years. This isotope is a significant environmental concern. What fraction of 90Sr produced today will remain after 100 years?

Radiocarbon Dating

Libby (1946) developed method of determining age using 146C. 14

6C is produced by cosmic radiation.

147N + 1

0n 146C + 1

1H 7.5 kg/year (~constant)

It decays: 14

6C 147N + 1

-1e t 1/2 = 5.73 x 103years

Initially, in live plant C-14 has 14 dpm of C(dpm = disintegrations/min/g) When the plant dies, the C-14 is not replaced and the disintegrations diminish.

Ex. The dead sea scrolls have 11 dpm. What is the age of the document?

Rules: 1) Up to atomic number 20, n=p is stable.

2) Above atomic number 20, n>p is stable.3) Above atomic number 84, all nuclei are unstable.4) Nuclei with 2, 8, 20, 28, 50, or 82 protons, or 2, 8, 20, 28, 50,

82, or 126 neutrons are particularly stable. These are the nuclear equivalent of closed shell configurations (and are called magic numbers).

5) Even numbers of protons and neutrons are more stable.

# of Stable Nuclei With This Configuration: # Protons # Neutrons 157 Even Even 52 Even Odd 50 Odd Even 5 Odd Odd

NUCLEAR STABILITY

NUCLEAR STABILITY

An isotope that is off the belt of stability can use four nuclear reactions to get to it:

1. 2. 3. positron emission4. electron capture

An isotope with a high n/p ratio is proton deficient.

To convert neutrons to protons, it can undergo -decay:

10n 1

1p + 0–1e

e.g. 9740Zr 97

41Nb + 0–1e

NUCLEAR STABILITY

i) Positron emission:1

1p 10n + 0

1e

e.g. 2011Na 20

10Ne + 01e

ii) Electron capture:1

1p + 0–1e 1

0n

Elements with atomic numbers greater than 84 undergo -decay in order to reduce both the numbers of neutrons and protons:

e.g. 23592U 231

90Th + 42He

An isotope with a low n/p ratio is neutron deficient.

To convert protons to neutrons, there are two possibilities:

NUCLEAR STABILITY contd.

238U DECAY

Cascade of and decay reactions

Moves diagonally down belt of stability

Eventually gets to stable isotope (206Pb)

2 11p + 2 1

0n 42He

11p mass is 1.00728 amu

10n mass is 1.00867 amu

42He mass is 4.00150 amu

Mass defect = (2)(1.00728 amu) + (2)(1.00867 amu) – 4.00150 amu = 0.03040 amu = 5.047x10-29 kg

Binding energy is the energy required to decompose the nucleus into nucleons (p and n): E = mc2

Probably better to write: E = (m)c2

E = (5.047x10-29kg) (3x108m/sec)2

NUCLEAR BINDING ENERGY

E = (5.047x10-29kg) (3x108m/sec)2 = 4.543x10-12J/4

2He = 2.736x1012J/mole 4

2He (huge compared to E for chemical reaction)

Binding energy per nucleon:

42He: 1.14x10-12J

5626Fe: 1.41x10-12J (largest - most stable nucleus)

23892U: 1.22x10-12J

Nuclei with mass greater than ~200 amu can fall apart exothermically – nuclear fission.

Combining light nuclei can be exothermic – nuclear fusion.

NUCLEAR BINDING ENERGY contd.

The rest masses of proton, neutron, and 12C nuclei are:

11p = 1.007276470 amu

11n = 1.008664904 amu

126C = 12 amu (exact)

Practice problem:

• Calculate the binding energy/mole of 12C.

• Calculate the binding energy/nucleon.

• Compare to E for combustion of one mole C.

Fission

23592U + 1

0n 13752Te + 97

40Zr + 210n

14256Ba + 91

36Kr + 310n

An average of 2.4 neutrons are produced per 235U.

Chain reactions:

Small: most neutrons are lost, subcritical mass.

Medium: constant rate of fission, critical mass,nuclear reactor.

Large: increasing rate of fission, supercritical mass, bomb.

NUCLEAR CHAIN REACTIONS

CRITICAL MASS

Nuclear reactor fuel is 238U enriched with 3% 235U.

This amount of 235U is too small to go supercritical.

The fuel is in the form of UO2 pellets encased in Zr or steel rods.

Liquid circulating in the reactor core is heated and is used to drive turbines. This liquid needs to be cooled after use, so reactors are generally near lakes and rivers.

NUCLEAR REACTORS

NUCLEAR REACTORS

Cadmium or boron are used in control rods because these elements absorb neutrons.

Moderators are used to slow down the emitted neutrons so that they can be absorbed by adjacent fuel rods.

Nuclear Fission Bombs

• Mainly U-235. Fortunately, U-235 is hard to purify

• Uranium ore is concentrated and treated with Fluorine to form UF6. This is low boiling and can be evaporated at 56 oC.

• 99.3% is non-fissionable U-238. Chemical reactions don’t help separate isotopes.

• Gaseous diffusion separates the heavier particles (UF6 with U-235 moves 0.4% faster than U-238)

• Repeated diffusion over long barriers or centrifugation concentrates U-235

• Breeder reactors- 238 U + n 239 Pu + 2e.

• Under Glenn Seaborg, Plutonium bomb was produced at Hanford, WA.

• Plutonium can be used for bombs or as a fuel source. However, small amounts of PuO2 dust in air causes lung cancer. Very toxic.

Breeder reactors are a second type of fission nuclear reactor.

A breeder reactor produces more fissionable material than it uses.

23994Pu and 233

92U are also fissionable nuclei and can be used in fission reactors.

23892U + 1

0n 23992U 239

93Np + 0–1e 239

94Pu + 0–1e

23290Th + 1

0n 23390Th 233

91Pa + 0-1e 233

92U + 0-1e

Breeder Reactors

Fusion “Chemistry of the stars”

The sun contains 73% H, and 26% He.

11H + 1

1H 21H + 0

+1e

11H + 2

1H 32He

32He + 3

2He 42He + 2

1H

32He + 1

1H 42He + 0

1e

Initiation of these reactions requires temperatures of 4x107K - not currently obtainable on a stable basis.

NUCLEAR REACTORS

Nuclear FusionTremendous amounts of energy are generated when light nuclei combine to form heavy nuclei-Sun (plasma ~106 K)

Short range binding energies are able to overcome the proton-proton repulsion in the nuclei

211H + 21

0n 42He

E= -2.73 x 1012 J/molBinding energy = +2.15 x 108 kJ/mol

Note: (covalent forces are only are fraction H-H bond E =436 kJ/mol)

The huge energy from 4 g of helium could keep a 100 Watt bulb lit for 900 years

H-bomb

63Li + 1

0n 31H + 4

2He

E= -1.7 kJ/mol/ mol tritium

The nucleons combine in a high energy plasma (~106

K).

A U-235 or Pu-239 bomb is set off first. A 20-megaton bomb has 300 lbs Li-D as well as a fission/atomic bomb.