Problem #0161 Quantum Physics Problem #0163 Chapters Chapters

863.

Problem 55.9 (RHK)

decays by alpha emission with a half-life of . It also decays (rarely) by spontaneous fission, and if the alpha decay did not occur, its half-life due to this process alone would be . (a) We have to find the rate with which spontaneous fission decays occur in 1.00 g of . We have to find the number of alpha-decay events that are there for every spontaneous fission event.

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The half-life of for alpha emission is . The disintegration constant for alpha emission will therefore be

.

The half-life of for spontaneous fission is .

The disintegration constant for spontaneous fission will therefore be

.

Number of nuclei in 1.00 g of are

The rate of spontaneous fissions in 1.00 g of will therefore be

Therefore, one spontaneous fission event will take place in

The rate of alpha emission in 1.00 g of will be

The number of alpha decays that will take place in 1.00 g of pure during the interval when one spontaneous fission occurs will therefore be