How much energy is needed for an electron revolving in the second orbit of He^+ ion, in order double — Atomic Structure Chemistry Question

💡 Solution & Explanation

To double the angular momentum from the second orbit (n_1 = 2), the electron must transition to the fourth orbit (n_2 = 4). The energy required for He^+ (Z = 2) is: Δ E = 13.6 * Z^2 * (1/n_1^2 - 1/n_2^2) = 13.6 * 4 * (1/4 - 1/16) = 10.2 eV (option c). Note: The printed key lists (b) 2.55 eV because of a book printing error where it incorrectly calculated the transition for Hydrogen (Z = 1) instead of He^+.