A electron of hydrogen atom on an excited state is having energy Eₙ=-0.85 eV. The maximum number of allowed transitions to lower energy level is _________.

Solution

Physics sir · 4 steps

Turn the energy into n first, then count every pair of levels the electron can jump between.

1. Find the level. For hydrogen, Eₙ = -13.6/n² eV. Setting this equal to -0.85 eV gives n² = 13.6/0.85 = 16, so n = 4.
2. Count the jumps. From n = 4 the electron can come down through levels 3, 2 and 1 in any order. Each allowed transition joins two different levels, so count the pairs of levels.

   N = n(n-1)/2 = (4 × 3)/2 = 6

3. List them. The six transitions are 4 → 3, 4 → 2, 4 → 1, 3 → 2, 3 → 1 and 2 → 1.
4. So. The maximum number of allowed transitions to lower levels is 6.

The common slip: 3. Counting only the direct jumps out of n = 4 (4 → 3, 4 → 2, 4 → 1) gives 3, not 6. The jumps between the lower levels count too.

The idea to keep. From level n, the total number of downward transitions (spectral lines) is n(n-1)/2, because each line joins one pair of levels. Get n from Eₙ = -13.6/n² eV first.

Answer from the NTA final answer key. Solution by PrepWiser.