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

No. of unique lines/wavelengths/ frequencies `=((n_(2)-n_(1))(n_(2)-n_(1)+1))/(2)`
If `e^(-)` is returning to ground state `(i.e. n_(1)=1)` then `["where" n_(2)=n]`
No. of unique lines `=((n-1)(n))/(2)`