Embibe Experts Solutions for Chapter: Nuclear Physics, Exercise 2: Exercise#2

A radioactive nucleus $A$ has a single decay mode with half life ${\tau }_{\mathrm{A}}$. Another radioactive nucleus $B$ has two decay modes, $1$ and $2$. If decay mode $2$ is absent, the half life of $B$ would be $\frac{{\mathrm{\tau }}_{\mathrm{A}}}{2}$. If decay mode $1$ is absent, the half life of $B$ would be $3{\tau }_{\mathrm{A}}$. If the actual half life of $B$ is ${\tau }_{\mathrm{B}}$, then the ratio $\frac{{\tau }_{\mathrm{B}}}{{\tau }_{\mathrm{A}}}$ is,

A nuclear decay is possible if the mass of the parent nucleus exceeds the total mass of the decay particles. If $M (A\text{,} Z)$ denotes the mass of a single neutral atom of an element with mass number $A$ and atomic number $Z$, then the minimal condition that the $\beta$ decay,

$X_Z^A\to Y_{Z+1}^A+{\beta }^{-}+{\overline{v}}_e$

will occur is ($m_{\mathrm{e}}$ denotes the mass of the $\beta$ particle and the neutrino mass $m_v$ can be neglected),

Two species of radioactive atoms are mixed in equal number. The disintegration of the first species is $\lambda$ and of the second is $\frac{\lambda }{3}$. After a long time, the mixture will behave as a species with mean life of approximately,

The half-life of a particle of mass $1.6\times {10}^{-26} \mathrm{kg}$ is $6.9 \mathrm{s}$ and a stream of such particles is travelling with the $\mathrm{K}.\mathrm{E}.$ of a particle being $0.05 \mathrm{eV}$. The fraction of particles which will decay when they travel a distance of $1 \mathrm{m}$ is,

The binding energy per nucleon of ${}_5\mathrm{B}^{10}$ is $8.0 \mathrm{MeV}$ and that of ${}_5\mathrm{B}^{11}$ is $7.5 \mathrm{MeV}$. The energy required to remove a neutron from ${}_5\mathrm{B}^{11}$ is (mass of electron and proton are $9.11\times {10}^{-31} \mathrm{kg}$ and $1.67\times {10}^{-27} \mathrm{kg}$, respectively),

The beta particles of a radioactive metal originate from,

A nuclear fuel rod generates energy at a rate of $5\times {10}^8 \mathrm{watt} {\mathrm{m}}^{-3}$. It is in the shape of a cylinder of radius $4.0 \mathrm{mm}$ and length $0.20 \mathrm{m}$. A coolant of specific heat $4\times {10}^3 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$ flows past it at a rate of $0.2 \mathrm{kg} {\mathrm{s}}^{-1}$. The temperature rise in this coolant is approximately,

The graph shows the log of activity $\left(\log R\right)$ of a radioactive material as a function of time $t$ in minutes.

The half-life (in $\min$) for the decay is closest to,