Find the number of spectral lines obtained when electron de-excites

CBSE Class 11
1

Find the number of spectral lines obtained when electron de-excites from 5th to the 1st energy level but no line is seen in Balmer series?

2

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
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