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Lecture 63 Nuclear Chemistry II

Review

- Decay DZ DA Dn Mode
- a -2 -4 -2
- b- 1 0 -1
- b -1 0 1
- EC -1 0 1
- g 0 0 0

Radioisotope Dating

- ratio of 14C to total C in the
- biosphere is a constant
- when an organism dies, exchange of 14C with the

biosphere stops - 14C in dead organism decreases

Radiocarbon Dating

e.g. the C14/C ratio in an artifact is 0.10 of

the ratio in living stuff. How old is

the artifact? t1/2 (14C) 5730 y

k 0.693/t1/2 1.21 x 10-4 y-1

ln (N/No) - kt

ln (0.10 / 1.0) -1.21 x 10-4 y-1 (t)

solving, t 19030 y

Nuclear Stability e.g. Pt (Z78)

N123

b- (n/p )

non-radioactive

b, EC (n/p )

a (n/p )

N90

Nuclear Stability

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neutrons needed for stability

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neutrons (N)

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N/Z1

Island of Stability

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0

protons (Z)

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90

Nuclear Stability

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b- decay

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neutrons needed for stability

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neutrons (N)

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N/Z1

Island of Stability

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a decay

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b, EC decay

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0

protons (Z)

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90

The Magic Numbers

- Very stable nuclei (large t1/2) if n or p
- 2, 8, 20, 28, 50, 82, 126
- (recall electron shells 2, 8, 18,)
- ? Shell Model of Nucleus

Decay Series

A ? B ? C ? D ? ... ? non-radioactive nuclide

There are three such series

A 238U, A 232Th, A 235U

and

238U Decay Series

a

b-

b-

a

238U ? 234Th ? 234Pa ? 234U ? 230Th

a

a

a

a

226Ra

222Rn(g)

218Po

214Pb

b-

b-

a

b-

214Bi ? 214Po ? 210Pb ? 210Bi

b-

a

210Po

206Pb

non-radioactive

Nuclear Reactions

- A B ? C

mass (A) mass (B) ¹ mass (C)

e.g.

find mass before and after reaction

Nuclear Reactions

mass before 26 mp 30 mn 26(1.00728 amu)

30(1.00866 amu) 56.44908 amu mass after mass

56Fe atom - 26 me 55.9349 amu - 26(.0005486

amu) 55.92070 amu

mass defect 0.52838 amu

Nuclear Reactions

The mass is converted to energy!

"It followed from the special theory of

relativity that mass and energy are both but

different manifestations of the same thing -- a

somewhat unfamiliar conception for the average

mind. Furthermore, the equation E is equal to m

c-squared, in which energy is put

equal to mass, multiplied by the square of the

velocity of light, showed that very small amounts

of mass may be converted into a very large amount

of energy and vice versa. The mass and energy

were in fact equivalent, according to the formula

mentioned before. This was demonstrated by

Cockcroft and Walton in 1932, experimentally."

Nuclear Reactions

The mass is converted to energy!

DE Dmc2

Dm 0.52838 amu / 56Fe nucleus 0.52838

g/mol 0.52838 x 10-3 kg/mol

c 3.00 x 108 m/s

Nuclear Reactions

DE Dmc2

0.52838 x 10-3 kg/mol (3.00 x 108 m/s)2

4.75 x 1013 (kg m2 s-2) / mol

4.75 x 1013 J/mol

4.75 x 1010 kJ/mol

the binding energy of 56Fe

Binding Energy

- is a maximum at 56Fe

heavier elements become more stable upon fission

lighter elements become more stable upon fusion

Energy of Nuclear Decay

e.g. 241Am 4He 237Np

241.0567 amu

237.0480 amu

4.0026 amu

Dm (4.0026 237.0480 - 241.0567)

-0.0061 amu

DE Dmc2 9.1 x 10-13 J / alpha particle

5.5 x 1011 J/mol

(very energetic particles)