The total number of $\alpha$ and $\beta$ particles emitted in the nuclear reaction ${ }_{92}^{238} \mathrm{U} \rightarrow{ }_{82}^{214} \mathrm{~Pb}$ is
$1$
$8$
$5$
$2$
The nucleus $_{48}^{115}Cd$ after two successive ${\beta ^ - }$ decays will give
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 |
A nucleus decays by ${\beta ^ + }$ emission followed by a gamma emission. If the atomic and mass numbers of the parent nucleus are $Z$ and $A$ respectively, the corresponding numbers for the daughter nucleus are respectively.
In a reactor, $2\, kg$ of ${ }_{92} U ^{235}$ fuel is fully used up in $30$ days. The energy released per fission is $200\, MeV.$ Given that the Avogadro number, $N =6.023 \times 10^{26}$ per kilo mole and $1\, eV =1.6 \times 10^{-19}\, J .$ The power output of the eactor is close to$.....MW$
A radioactive nucleus undergoes $\alpha$- emission to form a stable element. What will be the recoil velocity of the daughter nucleus if $V$ is the velocity of $\alpha$-emission and $A$ is the atomic mass of radioactive nucleus