Question

An element P disintegrates by $\alpha$ -emission and the new element suffers two further disintegrations, both by $\beta$ -emission, to form an element Q. Explain the fact that P and Q are the isotopes.

Answer 1

${}_X{P}^A-\alpha {\to }_{X-2}{M}^{A-4}$

${}_{X-2}{M}^{A-4}-\beta {\to }_{X-1}{N}^{A-4}$

${}_{X-1}{N}^{A-4}-\beta {\to }_X{Q}^{A-4}$

So, number of protons in $P$ and $Q$ are same, equal to $X$.

Number of neutrons in $P$ is $A-X$

Number of neutrons in $Q$ is $A-4-X$.

So, $P$ and $Q$ have equal number of protons but different number of neutrons. $P$ and $Q$ are thus isotopes.