How much energy would be required by an electron while moving from the ground state to the 3rd excit — Atomic Structure Chemistry Question

💡 Solution & Explanation

The 3rd excited state corresponds to $n=4$. For $He^+$, $Z=2$. $\Delta E = 13.6 \times Z^2 \times (1/n_1^2 - 1/n_2^2) = 13.6 \times 2^2 \times (1/1^2 - 1/4^2) = 13.6 \times 4 \times (15/16) = 13.6 \times 15/4 = 51.0 \text{ eV}$.