In the following equation representing $\beta^{-}$ decay,the number of neutrons in the nucleus $X$ is ${ }_{83}^{210} Bi \longrightarrow X + { }_{-1}^{0} e + \bar{\nu}$

The intensity of gamma radiation becomes $1/8$th of its initial value after traveling a distance of $36 \, mm$. After traveling what distance (in $mm$) will the intensity become half?

Which of the following is in the increasing order for penetrating power?

Sometimes a radioactive nucleus decays into a nucleus which itself is radioactive. An example is
$^{38}S \xrightarrow{2.48 \ h} ^{38}Cl \xrightarrow{0.62 \ h} ^{38}Ar$
Assume that we start with $1000$ $^{38}S$ nuclei at time $t = 0$. The number of $^{38}Cl$ nuclei is zero at $t = 0$ and will again be zero at $t = \infty$. At what value of $t$ would the number of $^{38}Cl$ nuclei be a maximum?

Give a brief explanation about radioactivity.

The nucleus ${ }_{88}^{226} Ra$ is converted into ${ }_{82}^{206} Pb$ by the emission of alpha $(\alpha)$ and beta $(\beta)$ particles. The number of alpha and beta particles emitted are respectively: