Net change in mass number during radioactive decay

Steps:

• Calculate original mass number: A = protons + neutrons = 92 + 143 = 235.
• Each α-particle removes 4 nucleons (2 protons + 2 neutrons), so 3 α-particles reduce A by 3 × 4 = 12.
• Each β⁻-particle converts a neutron to a proton but does not change total nucleons, so 4 β-particles reduce A by 0.
• Final mass number of nucleus X: A = 235 - 12 + 0 = 223.

Why D is correct:

• Not applicable; calculation yields ^{223}X, but options lack this—possibly a problem error.

Why the others are wrong:

• A: ^{231}X assumes only 1 α-particle (ΔA = -4), ignoring the other 2 α-decays.
• B: ^{218}X assumes excessive decay (ΔA = -17), not matching 3 α + 4 β.
• C: ^{222}X assumes 4 α-particles (ΔA = -16) or U-234 start, contradicting given neutrons.

Final answer: Not enough information.