The value of '' is — Atomic Structure Chemistry Question

💡 Solution & Explanation

$E_n - E_2 = 10.20 + 17.00 = 27.2$ eV. $E_n - E_3 = 4.25 + 5.9 = 10.15$ eV. Thus, $E_3 - E_2 = 27.2 - 10.15 = 17.05$ eV. We know $E_3 - E_2 = 13.6 Z^2 (\frac{1}{4} - \frac{1}{9}) = 13.6 Z^2 (\frac{5}{36})$. So $13.6 Z^2 (\frac{5}{36}) = 17.05 \implies Z^2 \approx 9 \implies Z = 3$. From $E_n - E_2 = 13.6 \times 9 \times (\frac{1}{4} - \frac{1}{n^2}) = 27.2 \implies 122.4 (\frac{1}{4} - \frac{1}{n^2}) = 27.2 \implies \frac{1}{4} - \frac{1}{n^2} = \frac{2}{9} \implies \frac{1}{n^2} = \frac{1}{36} \implies n = 6$. Therefore, correct answer is C.