How many different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms excited to states with principal quantum number n?

Explanation

From the `nth` state, the atom may go to `(n-1)` th state, …… 2nd state or 1st state. So there are different transitions. Similarly for other lower states. The total number of possible transitions is
`(n-1)+(n-2)+(n-3)+.......2+1`
`=(n(n-1))/(2)` (Remember)