Question

Show that n(n - 1)/2 different wavelength are observed in the hydrogen spectra if the atoms are excited to states with principal quantum numbers.

Answer 1

The Possible states when transition occur from nth state are (n–1)^th...... 2nd state or 1^st state, so there are (n–1) possible transitions starting from nth state. 

Further the atoms reaching the (n–1)^th state will make (n–2) different transitions. We can extend this reasoning further to other lower states.

Hence the possible number of transitions