Balancing atomic mass and number in decay chains Steps:

• Determine mass number change: final A = 207, initial A = 234, so ΔA = -27.
• Each α emission decreases A by 4; β emissions cause no change in A, so 4a = 27 gives a = 6.75 (non-integer).
• Atomic numbers of X and Y not given, so change in Z (where ΔZ = -2a + b) cannot be calculated.
• Not enough information to find integer a and b; process impossible as stated with only α and β emissions.

Why C is correct:

• Not enough information.

Why the others are wrong:

• A: Not enough information.
• B: Not enough information.
• D: Not enough information.

Final answer: Not enough information.