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

Explanation

To solve the problem of finding the transition in the hydrogen spectrum that has the same wavelength as the Balmer transition from \( n=4 \) to \( n=2 \) in the \( He^+ \) spectrum, we can follow these steps:

### Step 1: Understand the Formula for Wavelength in Hydrogen-like Atoms
The wavelength of the spectral lines in hydrogen-like atoms can be calculated using the formula:
\[ \frac{1}{\lambda} = RZ^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]
where:
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