How many unique spectral lines are emitted when `e^(-)` returns from `n_(2)^(th)` orbit to `n_(1)^(th)` orbit in a sample of H-like species ?

Explanation

To determine how many unique spectral lines are emitted when an electron returns from the \( n_2^{th} \) orbit to the \( n_1^{th} \) orbit in a sample of hydrogen-like species, we can use the formula for calculating the number of spectral lines emitted during transitions between energy levels.

### Step-by-Step Solution:

1. **Identify the orbits**: We have two energy levels, \( n_1 \) and \( n_2 \). We need to find the number of unique spectral lines emitted when an electron transitions from \( n_2 \) to \( n_1 \).

2. **Use the formula for spectral lines**: The general formula to calculate the number of unique spectral lines emitted when an electron transitions between two energy levels is given by:
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