Balancing mass number and atomic number in decay

Steps:

• Identify changes: mass number decreases by 4 (238 to 234); atomic number unchanged (both uranium, Z=92).
• Alpha decay effect: decreases mass by 4, atomic number by 2.
• Beta decay effect: no mass change, increases atomic number by 1.
• Solve equations: let n_α = number of alphas, n_β = number of betas; -4n_α = -4 so n_α=1; -2n_α + n_β=0 so n_β=2.

Why B is correct:

• Matches net change: one α decreases mass by 4 and Z by 2; two β increase Z by 2, restoring Z=92 while keeping mass at 234 (conservation in nuclear decays).

Why the others are wrong:

• A: Four α decrease mass by 16 (to 222) and Z by 8 (to 84, not uranium).
• C: Two α and eight β decrease mass by 8 (to 230) and net increase Z by 4 (to 96, not uranium).
• D: Identical to C, same incorrect net changes.

Final answer: B