how many spectral lines are seen for hydrogen atom when electron jump from n2=5 and n1=1  in visible region??

 

If the electron jumps from n₂ = 5 to n₁ = 1 then following are the transitions possible.

1. 5→ 4
2. 5→ 3
3. 5→ 2
4. 5 → 1
5. 4 → 3
6. 4→ 2
7. 4→ 1
8. 3 → 2
9. 3→ 1
10. 2 → 1

Hence there are 10 transitions and hence 10 spectral lines possible.

The general formula for the number of spectral lines emitted is

N = (n₂ – n₁) (n₂ – n₁ + 1)

2

So N = ( 5 - 1) ( 5 - 1 + 1 ) = 4 X 5 = 10

2 2