The isotope ${ }_5^{12} \mathrm{~B}$ having a mass $12.014 \mathrm{u}$ undergoes $\beta$-decay to ${ }_6^{12} \mathrm{C} .{ }_6^{12 .}$ has an excited state of the nucleus $\left({ }_6^{12} \mathrm{C}^*\right)$ at $4.041 \mathrm{MeV}$ above its ground state. If ${ }_5^{12} \mathrm{~F}$ decays to ${ }_6^{12} \mathrm{C}^*$, the maximum kinetic energy of the $\beta$-particle in units of $\mathrm{MeV}$ is ( $1 \mathrm{u}=931.5 \mathrm{MeV} / c^2$, where $c$ is the speed of light in vacuum).
$5$
$9$
$3$
$1$
In an $\alpha -$ decay, the kinetic energy of $\alpha -$ particle is $48\, MeV$ and $Q$ value of the reaction is $50\, MeV$. The mass number of the mother nucleus is [assume that daughter nucleus is inground state]
Explain the basic nuclear process by equation in $\beta -$ decay.
$_1{H^1}{ + _1}{H^1}{ + _1}{H^2} \to X + {\;_{ + 1}}{e^0} + $energy. The emitted particle is
List-$I$ shows different radioactive decay processes and List-$II$ provides possible emitted particles. Match each entry in List-$I$ with an appropriate entry from List-$II$, and choose the correct option.
List-$I$ | List-$II$ |
($P$) ${ }_{92}^{238} U \rightarrow{ }_{91}^{234} \mathrm{~Pa}$ | ($1$) one $\alpha$ particle and one $\beta^{+}$particle |
($Q$) ${ }_{82}^{214} \mathrm{~Pb} \rightarrow{ }_{82}^{210} \mathrm{~Pb}$ | ($2$) three $\beta^{-}$particles and one $\alpha$ particle |
($R$) ${ }_{81}^{210} \mathrm{Tl} \rightarrow{ }_{82}^{206} \mathrm{~Pb}$ | ($3$) two $\beta^{-}$particles and one $\alpha$ particle |
($S$) ${ }_{91}^{228} \mathrm{~Pa} \rightarrow{ }_{88}^{224} \mathrm{Ra}$ | ($4$) one $\alpha$ particle and one $\beta^{-}$particle |
($5$) one $\alpha$ particle and two $\beta^{+}$particles |
When $_3Li^7$ nuclei are bombarded by protons, and the resultant nuclei are $_4Be^8$, the emitted particles will be