Conservation of protons and neutrons in nuclear reactions Steps:

• Calculate total protons (Z): 16 (from S) + 42 (from Mo) = 58; alpha has 2 protons, so X has 58 - 2 = 56 protons.
• Calculate total neutrons: 32 - 16 = 16 (S) + 92 - 42 = 50 (Mo) = 66; alpha has 2 neutrons, so X has 66 - 2 = 64 neutrons.
• Mass number of X: 56 protons + 64 neutrons = 120, so X is ^{120}_{56} (barium nucleus).
• The choice identifies the neutron number of X as 64.

Why A is correct:

• A gives 64, matching the neutrons in X via conservation of neutron number (total neutrons minus those in alpha particle).

Why the others are wrong:

• B (54): Underestimates neutrons by not accounting for all from Mo (50) plus S (16) minus 2.
• C (18): Matches only S neutrons plus alpha protons, ignoring Mo and conservation.
• D (95): Approximates Mo mass but ignores S addition and alpha emission.

Final answer: A