Balancing mass and atomic numbers in decay Steps:

• Mass number change: 221 (Fr) - 209 (Bi) = 12; each α removes 4, so 3 α particles needed.
• Atomic number change: 87 (Fr) - 83 (Bi) = -4; each α decreases Z by 2, each β increases Z by 1.
• For 3 α: Z change -6; need net -4, so 2 β particles give +2, totaling -4.
• Verify: mass loss 3×4=12; Z change -2×3 +1×2=-4, matches.

Why D is correct:

• Matches conservation laws: mass number decreases by exactly 12, atomic number by 4 via α and β emissions.

Why the others are wrong:

• A and C (identical): 2 α lose only 8 mass (need 12); Z change -4 +4=0 (need -4).
• B: 3 α lose 12 mass (correct), but Z change -6 +4=-2 (need -4).

Final answer: D