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

$A$ radioactive nucleus decays as follows:
$X \xrightarrow{\alpha} X_1 \xrightarrow{\beta} X_2 \xrightarrow{\alpha} X_3 \xrightarrow{\gamma} X_4$
If the atomic number and the mass number of $X$ are $72$ and $180$ respectively,then the mass number and atomic number of $X_4$ are:

$A$ radioactive nucleus is initially at rest. It decays by emitting an electron and a neutrino at right angles to each other. The momentum of the electron is $3.2 \times 10^{-23} \ kg \cdot m/s$ and the momentum of the neutrino is $6.4 \times 10^{-23} \ kg \cdot m/s$. What is the direction of the recoil of the nucleus with respect to the direction of the electron?

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

If $Alpha$,$Beta$,and $\Gamma$ rays carry the same momentum,which has the longest wavelength?

$A$ radioactive decay can form an isotope of the original nucleus with the emission of which particles?