Nuclear Fission: The Basic Process — Question 1

Question 1

Conservation identifies the missing fragment in a fission channel

An illustrative channel is $^{235}_{92}\mathrm U+n\to{}^{141}_{56}\mathrm{Ba}+{}^{A}_{Z}X+3n$. Subsequent beta-minus decays change nuclear charge without changing A.

1. Identify A, Z and the element X (Z=36 is krypton).

2. If the A=141 fragment undergoes three beta-minus decays, write the net nuclear and lepton bookkeeping.

Question 1 - Solution

Conservation identifies the missing fragment in a fission channel

(a) Method and calculation

$$235+1=141+A+3\Rightarrow\boxed{A=92}.$$$$92=56+Z\Rightarrow\boxed{Z=36,\quad X={}^{92}_{36}\mathrm{Kr}}.$$

(b) Interpretation and further calculation

$$\boxed{{}^{141}_{56}\mathrm{Ba}\to{}^{141}_{59}\mathrm{Pr}+3e^-+3\bar\nu_e}.$$$$Q_{\mathrm{charge}}:\ 56=59-3;\qquad L:\ 0=3-3.$$

Physical check

Fission produces a distribution of channels. Mass number counts nucleons, not rest mass, so its conservation does not imply zero released energy.