Net atomic number change must be zero for isotopes Steps:

• Isotopes share the same atomic number Z but differ in mass number A.
• Each α decay reduces Z by 2 and A by 4.
• Each β⁻ decay increases Z by 1 with no A change.
• Net ΔZ = -2(n_α) + n_β = 0 requires n_β = 2 n_α; net ΔA = -4 n_α ≠ 0 ensures different isotopes. Why C is correct:
• 1 α and 2 β yield ΔZ = -2 + 2 = 0 (same Z per isotope definition) and ΔA = -4 (different A). Why the others are wrong:
• A: ΔZ = -2 ≠ 0, changes element.
• B: ΔZ = -4 ≠ 0, changes element.
• D: ΔZ = -4 + 1 = -3 ≠ 0, changes element.

Final answer: C