Which one of the following is a possible nuclear reaction?

In $\beta^{-}$ decay, a neutron transforms into a proton within the nucleus according to the equation:
$\text{neutron} \rightarrow \text{proton} + \beta^{-} + x$
In this equation, the particle represented by '$x$' is:

$A$ nuclear decay is possible if the mass of the parent nucleus exceeds the total mass of the decay particles. If $M(A, Z)$ denotes the mass of a single neutral atom of an element with mass number $A$ and atomic number $Z$,then the minimal condition that the $\beta^{-}$ decay $X_Z^A \rightarrow Y_{Z+1}^A + \beta^{-} + \bar{\nu}_e$ will occur is ($m_e$ denotes the mass of the $\beta^{-}$ particle and the neutrino mass $m_{\nu}$ can be neglected).

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

$A$ 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:

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?