Question

In a nuclear fission reaction of an isotope of mass M, three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect \(\triangle M\) will be 

(1) \(\sqrt {\frac {2c\triangle M}{M}}\)

(2) \(\frac {\triangle Mc ^2}{3}\)

(3) \(c\sqrt {\frac {2 \triangle M}{M}}\)

(4) \(c\sqrt {\frac {3\triangle M}{M}}\)

Answer 1

(3) \(c\sqrt {\frac {2 \triangle M}{M}}\)

\(\underset {M}{(X)} \rightarrow \underset {M/3}{(Y)} + \underset {M/3}{(Z)} + \underset {M/3}{(P)}\)

\(\triangle Mc^2 = \frac {1}{2}\frac {M}{3} V^2 + \frac {1}{2} \frac {M}{3}V^2 + \frac {1}{2} \frac {M}{3} V^2\)

\(V =c\sqrt {\frac {2 \triangle M}{M}}\)