Question

What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition, \( n = 4 \) to \( n = 2 \) of He\(^+\) spectrum?

• A. \( n = 4 \) to \( n = 2 \)
• B. \( n = 3 \) to \( n = 2 \)
• C. \( n = 2 \) to \( n = 1 \)
• D. \( n = 3 \) to \( n = 3 \)

Hint:

The wavelengths of transitions in hydrogen-like atoms are related to the change in energy levels and can be calculated using the Rydberg formula.

Answer 1

The Correct Option is C

Step 1: Understanding the transitions.
The wavelength of the transition is determined by the change in energy levels. For He\(^+\), the wavelength of the transition from \( n = 4 \) to \( n = 2 \) will match the transition from \( n = 2 \) to \( n = 1 \) in the hydrogen spectrum.

Step 2: Conclusion.
The correct transition is from \( n = 2 \) to \( n = 1 \), corresponding to option (3).