Question

A heavy nucleus $N$, at rest, undergoes fission $N \rightarrow P + Q$, where $P$ and $Q$ are two lighter nuclei Let $\delta= M _{ N }$ - $M_{P}-M_{Q}$, where $M_{P}, M_{Q}$ and $M_{N}$ are the masses of $P, Q$ and $N$, respectively $E _{P}$ and $E_{Q}$ are the kinetic energies of $P$ and $Q$, respectively. The speeds of $P$ and $Q$ are $v_{P}$ and $v_{Q}$, respectively If $c$ is the speed of light, which of the following statement(s) is(are) correct?

• A. $E_{p}+E_{Q}=c^{2} \delta$
• B. $E_{p}=\left(\frac{M_{p}}{M_{p}+M_{Q}}\right) c^{2} \delta$
• C. $\frac{ v _{ P }}{ v _{ Q }}=\frac{ M _{ Q }}{ M _{ P }}$
• D. The magnitude of momentum for $P$ as well as $Q$ is $c \sqrt{2 \mu \delta}$, where $\mu=\frac{ M _{ p } M _{ Q }}{\left( M _{ p }+ M _{ Q }\right)}$

Answer 1

The Correct Option is D

D

The magnitude of momentum for $P$ as well as $Q$ is $c \sqrt{2 \mu \delta}$, where $\mu=\frac{ M _{ p } M _{ Q }}{\left( M _{ p }+ M _{ Q }\right)}$