After the decay of a single $\beta$ particle, the parent and daughter nuclei are

Statement-$1$: $A$ nucleus having energy $E_{1}$ decays by $\beta^{-}$ emission to a daughter nucleus having energy $E_{2}$,but the $\beta^{-}$ rays are emitted with a continuous energy spectrum having an end-point energy $E_{1} - E_{2}$.
Statement-$2$: To conserve energy and momentum in $\beta$ decay,at least three particles must take part in the transformation.

$A$ nucleus $_n{X^m}$ emits one $\alpha$ and one $\beta$ particle. The resulting nucleus is:

How many alpha and beta particles are emitted when Uranium ${}_{92}U^{238}$ decays to lead ${}_{82}Pb^{206}$?

Consider a radioactive nucleus $A$ which decays to a stable nucleus $C$ through the following sequence: $A \to B \to C$. Here $B$ is an intermediate nucleus which is also radioactive. Considering that there are $N_0$ atoms of $A$ initially,plot the graph showing the variation of the number of atoms of $A$ and $B$ versus time.

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