Nuclear Fission: The Basic Process — Question 7

Question 7

A fission-product yield links a burst to later activity

A short burst contains $2.00\times10^{10}$ fissions. One radioactive product has independent yield .0600 nucleus per fission and half-life 2.00 h. Ignore parent feeding and loss of product atoms.

1. Calculate its initial inventory and initial activity in becquerels.

2. Find its activity after 6 h and the number of its decays in that interval.

Question 7 - Solution

A fission-product yield links a burst to later activity

(a) Method and calculation

$$\boxed{N_0=.0600(2.00\times10^{10})=1.20\times10^9},\quad\lambda=\ln2/7200\,\mathrm{s^{-1}}.$$$$\boxed{A_0=\lambda N_0=1.15525\times10^5\,\mathrm{Bq}}.$$

(b) Interpretation and further calculation

$$\boxed{A(6\,\mathrm h)=A_0\,2^{-3}=1.44406\times10^4\,\mathrm{Bq}}.$$$$\boxed{N_{\mathrm{dec}}=N_0(1-2^{-3})=1.05\times10^9}.$$

Physical check

Independent yield counts directly formed nuclei. A cumulative yield would require careful treatment of precursors to avoid double counting.