The number of spectral lines that are possible when electrons in 7th shell in different hydrogen atoms return to the 2nd shell is

Number of spectral lines ={[n₂ -n₁]  [n₂ -n₁+1]}/2

When electrons in 7^th shell to 2^nd shell (n₁= 2 ;n₂ =7)

Number of spectral lines = {[7-2][7-2+1]}/2 

Number of spectral lines ={[5][6]}/2

=15