Net atomic number change must be zero for isotope formation

Steps:

• Alpha decay decreases atomic number Z by 2; beta decay increases Z by 1.
• For an isotope of the original element, net ΔZ = 0 after all decays.
• Let a = number of alphas, b = number of betas; solve -2a + b = 0, so b = 2a.
• Total particles n = a + b = 3a; minimum n=3 when a=1, b=2.

Why B is correct:

• Minimum emissions satisfying -2a + b = 0 yield n=3, per decay definitions.

Why the others are wrong:

• A: No combination of 2 particles gives net ΔZ=0 (e.g., 2 betas: +2; 1 each: -1).
• C: Possible but not minimum (e.g., a=0, b=4: +4 ≠0; requires more than 3).
• D: Exceeds minimum; unnecessary for net ΔZ=0.

Final answer: B