A nucleus with $Z = 92$ emits the following in a sequence: $\alpha ,\,{\beta ^ - },\,{\beta ^ - },\,\alpha ,\alpha ,\alpha ,\alpha ,\alpha ,{\beta ^ - },\,{\beta ^ - },\alpha ,\,{\beta ^ + },\,{\beta ^ + },\,\alpha $. The $Z$ of the resulting nucleus is

Assertion: ${}_Z{X^A}$ undergoes a $2\alpha  -$ decays, $2\beta  -$ decays and $2\gamma  - $ decays and the daughter product is ${}_{Z - 2}{X^{A - 8}}$

Reason : In $\alpha  - $decays the mass number decreases by $4$ and atomic number decreases by $2$. In $2\beta  - $ decays the mass number remains unchanged, but atomic number increases by $1$ only.

When a nucleus with atomic number $Z$ and mass number $A$ undergoes a radioactive decay process :

The composition of an $\alpha $- particle can be expressed as

In a radioactive decay chain, the initial nucleus is ${}_{90}^{232}Th$.  At the end there are $6\,\,\alpha -$ particles and $4\,\,\beta -$ particles with are emitted. If the end nucleus is ${}_Z^AX\,,\,A$ and $Z$ are given by

A nucleus of atomic mass $A$ and atomic number $Z$ emits ${M_1}$ particles. The atomic mass and atomic number of the resulting nucleus are