Nuclear Decay and Conservation Laws Steps:

• Uranium-238 has mass number 238 and atomic number 92 (Z=92 for U).
• Each α-particle emission reduces mass by 4 and Z by 2; two α-particles: mass decreases by 8, Z by 4.
• One β-particle emission keeps mass the same but increases Z by 1.
• Final mass number: 238 - 8 = 230; final Z: 92 - 4 + 1 = 89 (Ac has Z=89).

Why B is correct:

• ^{230}Ac matches the calculated mass number 230 and Z=89 after the specified decays, per conservation of nucleon and charge numbers.

Why the others are wrong:

• A (^{227}Ac): Mass too low; ignores full effect of only two α-decays (would require three for -12).
• C (^{231}Ac): Mass too high; overcounts β-effect or undercounts α-decays.
• D (^{234}Ac): Mass even higher; equivalent to only one α-decay, not two.

Final answer: B