A single electron species has a stationary nucleus. The energy required to excite the electron from — Atomic Structure Chemistry Question

💡 Solution & Explanation

The energy of an electron in the $n^{th}$ orbit is $E_n = -13.6 \frac{Z^2}{n^2} \text{ eV}$. For $Be^{3+}$ ($Z=4$), the energy difference is $\Delta E = E_4 - E_3 = 13.6 \times 4^2 \times (\frac{1}{3^2} - \frac{1}{4^2}) = 13.6 \times 16 \times (\frac{1}{9} - \frac{1}{16}) = 13.6 \times 16 \times \frac{7}{144} = 13.6 \times \frac{7}{9} \approx 10.577 \text{ eV} \approx 10.58 \text{ eV}$.