Pauli suggested the emission of neutrino during $\beta^{+}$ decay to explain:

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?

$A$ hypothetical radioactive nucleus decays according to the following series:
$A \xrightarrow{\alpha} A_1 \xrightarrow{\beta^-} A_2 \xrightarrow{\alpha} A_3 \xrightarrow{\gamma} A_4$
If the mass number and atomic number of $A$ are respectively $180$ and $72$,then the atomic number and mass number of $A_4$ will be respectively:

In gamma ray emission from a nucleus,

Give a brief explanation about radioactivity.

${ }_{90}^{232} \text{Th}$ emits $6 \alpha$ and $4 \beta$ particles and gets converted into lead. The mass number and atomic number of lead is $......$