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Correct answer: Ionization energy of X^(+2)(g)
The process is: X^(+1)(g) → X^(+2)(g) + e⁻, energy absorbed = 4 eV. The ionization energy of a species is the energy required to remove the outermost electron from that species in gaseous state. Here, we are removing an electron from X^(+1)(g) to give X^(+2)(g). This is by definition the second ionization energy of X(g) [IE2] or equivalently the first ionization energy of X^(+1)(g). None of the options say 'IE of X^(+1)(g)' directly. Option B says 'IE of X^(+2)(g)' which would be X^(+2)(g) → X^(+3)(g) + e⁻ — that is different. Option C says 'IE of X(g)' = X(g) → X^(+1)(g) + e⁻ — that is also different. Option D: electron gain enthalpy of X^(+2)(g) = energy when X^(+2)(g) gains an electron to become X^(+1)(g). For a reverse process: X^(+2)(g) + e⁻ → X^(+1)(g), energy released = 4 eV. So |electron gain enthalpy of X^(+2)(g)| = 4 eV. This matches! Answer: magnitude of electron gain enthalpy of X^(+2)(g).