Balancing mass number and atomic number in decay chain

Steps:

• Mass number change: 238 - 206 = 32; each α-particle reduces mass by 4, so α-particles = 32 / 4 = 8.
• Atomic number: U (Z=92) to Pb (Z=82), net change = -10.
• Each α-particle reduces Z by 2, so 8 α-particles reduce Z by 16.
• Each β-particle increases Z by 1, so β-particles = 16 - 10 = 6 to achieve net -10.

Why A is correct:

• Matches conservation: 8 α-particles account for mass loss of 32; net Z change = -2(8) + 6 = -10, per decay rules.

Why the others are wrong:

• B: 10 β-particles give net Z = -16 + 10 = -6 (not -10).
• C: 16 α-particles give mass loss of 64 (exceeds 32).
• D: 16 α-particles and 22 β-particles give mass loss of 64 and net Z = -32 + 22 = -10 (mass wrong).

Final answer: A