The value of Rydberg constant , if He ions are known to have the wavelength difference between the f — Atomic Structure Chemistry Question

💡 Solution & Explanation

For He$^+$ ($Z=2$): First Balmer line $\lambda_B = \frac{36}{5 R Z^2} = \frac{36}{20R} = \frac{1.8}{R}$. First Lyman line $\lambda_L = \frac{4}{3 R Z^2} = \frac{4}{12R} = \frac{1}{3R}$. The difference $\Delta\lambda = \frac{1.8}{R} - \frac{0.333}{R} = \frac{1.466}{R} = 132 \times 10^{-9}$ m. Solving gives $R = \frac{1.466}{132 \times 10^{-9}} \approx 1.11 \times 10^7 \text{ m}^{-1}$. Therefore, correct answer is B.