An atom has a mass number of $232$ and an atomic number of $90$. How many $\alpha$-particles should it emit after the emission of two $\beta$-particles,so that the resulting atom has a mass number of $212$ and an atomic number of $82$?

In the decay sequence:
$^{238}_{92}U$ $\xrightarrow{- x_1} ^{234}_{90}Th$ $\xrightarrow{- x_2} ^{234}_{91}Pa$ $\xrightarrow{- x_3} ^{234}_{92}Z$ $\xrightarrow{- x_4} ^{230}_{90}Th$
$x_1, x_2, x_3$ and $x_4$ are particles/radiation emitted by the respective isotopes. The correct option$(s)$ is/are-
$(1)$ $Z$ is an isotope of uranium
$(2)$ $x_2$ is $\beta^{-}$
$(3)$ $x_1$ will deflect towards negatively charged plate
$(4)$ $x_3$ is $\gamma$-ray

If it is assumed that ${}_{92}^{235}U$ decays only by emitting $\alpha$ and $\beta$ particles,the possible product of the decay is:

During a $\beta$-decay,the mass of the atomic nucleus

$\beta$-particles are emitted from the atom

$_{72}^{180}X$ $\xrightarrow{2\alpha}$ $\xrightarrow{\beta}$ $\xrightarrow{\gamma} _{Z}^{A}X'$. The values of $Z$ and $A$ are: