The order of ionization potential between He+ ion and H-atom (both species are in gaseous state) is — Periodic Table and Periodicity Chemistry Question

💡 Solution & Explanation

# Ionization Potential Comparison: $He^+$ vs $H^-$ **Step 1: Identify what we're comparing** - $He^+$ ion: helium with one electron removed (hydrogen-like, Z = 2) - $H^-$ ion: hydrogen with an extra electron (two electrons, Z = 1) **Step 2: Apply the ionization potential formula for hydrogen-like species** For hydrogen-like ions: $$IP = 13.6 \times Z^2 \text{ eV}$$ For $He^+$: $$IP = 13.6 \times 2^2 = 54.4 \text{ eV}$$ **Step 3: Determine ionization potential of $H^-$** $H^-$ has two electrons with higher electron-electron repulsion. Removing one electron from $H^-$ requires much less energy because: - The remaining electron experiences significant repulsion from the departing electron - Effective nuclear charge is very small (only Z = 1) Experimentally: $$IP(H^-) = 0.75 \text{ eV}$$ **Step 4: Compare** $$He^+ \text{ (54.4 eV)} \gg H^- \text{ (0.75 eV)}$$ **Conclusion:** The order is: **$IP(He^+) > IP(H^-)$** The $He^+$ ion has a much higher ionization potential because its higher nuclear charge (Z=2) pulls strongly on its single electron, making it much harder to remove.