excited hydrogen atom emits a Photon of wave length in returning to the ground state The quantum number n of exilted state is given by
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Explanation
$ {1 \over \lambda} R [{ 1 \over 1 ^2 } - { 1 \over n^2 } ] $ $ {1 \over \lambda } = R [ 1- { 1 \over n^2 } ]$ $ { 1 \over \lambda } = R - { R/ n^2}$ $ { R \over n^2 }= R -{1/ \lambda } = { \lambda R -1 \over \lambda }$ $ { R \over n^2 } = { \lambda R -1 \over \lambda}$ $ n^2 = { \lambda R \over \lambda R -1 }$ $ n = \sqrt {\lambda R \over \lambda R -1}$