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 let state are `(n - 1)` possible transition starting from the nth state The atom reaching `(n - 1)`th state make `(n- 2)`different transition similarly for other lower states The total number of possible transition is
`(n - 1) +(n - 2) + (n - 3)+...2+ 1`
`= (n(n - 1))/(2)`