The number of spectral lines that are possible when electrons in 7^th shell in of hydrogen atom return to the 2^nd shell in multiple steps are

Assuming that the transitions occur in multiple steps,

No. of spectral lines  =$\frac{\mathrm{n}(\mathrm{n}+1)}{2}$

Where, n = n₂ - n₁

           n = 7 - 2 = 5

Number of spectral lines =$\frac{5(5+1)}{2}$= 15