question_answer

In a radioactive decay, a nucleus emits an \[\alpha \]-particle and two \[\beta \]-particles successively. Show that the final nucleus is an isotope of the original nucleus.

Answer:

                The entire decay process may be represented as \[\frac{A}{Z}X\xrightarrow{_{2}^{4}He}_{Z}^{A}_{-2}^{-4}\Upsilon \xrightarrow{_{-1}^{0}e}_{Z}^{A}_{-1}^{-4}Z\xrightarrow{_{-1}^{0}e}A-_{Z}^{4}X'\] As both \[\text{X}'\] and \[\text{X}\] have the same atomic number Z, so the final nucleus is an isotope of the original nucleus.