A radioactive element A decays into radioactive element C by the following processes in succession. $\mathrm{A} \rightarrow \mathrm{~B}+{ }_2 \mathrm{H}_{\mathrm{e}}^4 ; \mathrm{B} \rightarrow \mathrm{C}+2 \mathrm{e}^{-}$ Then elements

Analyzing the radioactive decay chain of element $A = _Z^M A$:

Alpha decay: $A \rightarrow B + _2^4 \text{He}$
By conservation: mass number $M = M_B + 4 \Rightarrow M_B = M - 4$
Atomic number $Z = Z_B + 2 \Rightarrow Z_B = Z - 2$
Thus $B = _{Z-2}^{M-4} B$

Beta decay (2$\beta^-$): $B \rightarrow C + 2\ _{-1}^0 e$
Mass number: $M - 4 = M_C$
Atomic number: $Z - 2 = Z_C - 2 \Rightarrow Z_C = Z$
Thus $C = _Z^{M-4} C$

$A$ and $C$ share atomic number $Z$ but differ in mass number ($M$ vs. $M-4$), confirming they are isotopes.