A nucleus X of mass number 238 undergoes 3 α-decays

Solution

To determine the mass number and atomic number of the final nucleus after a series of nuclear decays, we apply the changes caused by each type of decay: Given: • Initial nucleus: X, mass number = 238, let atomic number = Z (not specified, but final options indicate it is probably Uranium-238, so Z = 92) Effect of 3 α-decays Each α-decay reduces: • Mass number (A) by 4 • Atomic number (Z) by 2 After 3 α-decays: • Mass number: 238 − (3 × 4) = 226 • Atomic number: 92 − (3 × 2) = 86 Effect of 2 β⁻-decays: Each β⁻-decay: • Converts a neutron into a proton • Atomic number increases by 1 • Mass number remains unchanged After 2 β⁻-decays: • Atomic number: 86 + 2 = 88 • Mass number: remains 226 Final result: • Mass number = 226 • Atomic number = 88