The intensity of gamma radiation from a given source is $I$. On passing through $36 \, mm$ of lead,it is reduced to $\frac{I}{8}$. The thickness of lead which will reduce the intensity to $\frac{I}{2}$ will be......$mm$

Write nuclear reaction equations for:
$(i)$ $\alpha$-decay of $^{226}_{88}Ra$
$(ii)$ $\alpha$-decay of $^{242}_{94}Pu$
$(iii)$ $\beta^-$-decay of $^{32}_{15}P$
$(iv)$ $\beta^-$-decay of $^{210}_{83}Bi$
$(v)$ $\beta^+$-decay of $^{11}_{6}C$
$(vi)$ $\beta^+$-decay of $^{97}_{43}Tc$
$(vii)$ Electron capture of $^{120}_{54}Xe$

Obtain the maximum kinetic energy of $\beta$-particles and the radiation frequencies of $\gamma$-decays in the decay scheme shown in the figure. You are given that:
$m(^{198}Au) = 197.968233 \; u$
$m(^{198}Hg) = 197.966760 \; u$

Which of the following is not a mode of radioactive decay?

Which of the following is deflected by an electric field?

The nucleus ${ }_{Z}^{A} X$ undergoes the series of reactions given below:
${ }_{Z}^{A} X \stackrel{\alpha \text {-decay }}{\longrightarrow} P \stackrel{\beta \text {-decay }}{\longrightarrow} Q \stackrel{\alpha \text {-decay }}{\longrightarrow} R$
The number of neutrons in the nucleus $R$ is