Atomic StructureHard

Question

The value of Rydberg constant R, if He+ ions are known to have the wavelength difference between the first (of the longest wavelength) lines of the Balmer and Lyman series equal to 132 nm, is

Options

A.2.07 × 1016 m–1
B.1.11 × 107 m−1
C.9 × 10−8 m−1
D.1.936 × 107 m−1

Solution

$\frac{1}{\lambda_{1}} = R \times 2^{2}\left( \frac{1}{2^{2}} - \frac{1}{3^{2}} \right) \Rightarrow \lambda_{1} = \frac{9}{5R}$

$\frac{1}{\lambda_{2}} = R \times 2^{2}\left( \frac{1}{1^{2}} - \frac{1}{2^{2}} \right) \Rightarrow \lambda_{2} = \frac{1}{5R}$

From question, $\lambda_{1} - \lambda_{2}$=132 nm

$\text{Or, }\frac{9}{5R} - \frac{1}{3R} = 132 \times 10^{- 9}\text{ m } \Rightarrow \text{R=1.11} \times \text{1}\text{0}^{9}\text{ }\text{m}^{- 1}$

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