Question

The wave number of the limiting line in Lyman series of hydrogen is \(109678\,\text{cm}^{-1}\). The wave number of the limiting line in Balmer series of He\(^+\) would be:

• A. \(54839\,\text{cm}^{-1}\)
• B. \(109678\,\text{cm}^{-1}\)
• C. \(219356\,\text{cm}^{-1}\)
• D. \(438712\,\text{cm}^{-1}\)

Hint:

Wave number scales as \(Z^2\) for hydrogen-like ions.

Answer 1

The Correct Option is D

Step 1: For hydrogen-like species: \[ \bar{\nu} = R Z^2 \left(\frac{1}{n_1^2}\right) \]
Step 2: For He\(^+\), \(Z=2\), Balmer series \(n_1=2\).
Step 3: \[ \bar{\nu} = 109678 \times \frac{4}{(2)^2} = 4 \times 109678 \]