The wavelength of the first line of Lyman series for hydrogen is idetical to that of the second line of Balmer series for some hydrogen like ion Y. Calculate energies of the first three levels of Y.

Explanation

To solve the problem, we need to find the energies of the first three levels of a hydrogen-like ion Y, given that the wavelength of the first line of the Lyman series for hydrogen is identical to that of the second line of the Balmer series for the ion Y.

### Step-by-Step Solution:

1. **Identify the transitions for the Lyman and Balmer series**:
- The first line of the Lyman series corresponds to the transition from \( n_i = 2 \) to \( n_f = 1 \).
- The second line of the Balmer series corresponds to the transition from \( n_i = 4 \) to \( n_f = 2 \).

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