The electron in a hydrogen atom is excited to the n -th excited state. How many possible spectral lines can it emit in transtion to the ground state ?

Explanation

There are n number of states from the n-th quantum state to the ground state (n=1). Transition may occur between any pair of these states.
Since for each transition a spectral line is formed , the number of possible spectral lines `="^nC_2=(n(n-1))/(1xx2)=1/2n(n-1)`.