According to Bohr atomic model, in which of the following transitions will the frequency be maximum?

Solution

Physics sir · 2 steps

Frequency follows the energy gap, and Bohr levels crowd together as n grows, so the lowest jump wins.

1. Frequency from gap. The emitted photon carries the energy difference between the two levels, hν = E_(n₂) - E_(n₁). A bigger gap means a higher frequency.

   ν ∝ 1/n₁² - 1/n₂²

   Transition	1/n₁² - 1/n₂²	Value
   (a) 2 to 1	1 - 1/4 = 3/4	0.75
   (b) 3 to 2	1/4 - 1/9 = 5/36	0.139
   (c) 4 to 3	1/9 - 1/16 = 7/144	0.049
   (d) 5 to 4	1/16 - 1/25 = 9/400	0.0225

2. So. The gap between n = 2 and n = 1 is far larger than any of the others, so the transition from n = 2 to n = 1 gives the maximum frequency: option (a).

The idea to keep. Since Eₙ ∝ -1/n², energy levels get closer together as n increases. For jumps of one step, the one landing on the lowest level always has the largest gap and the highest frequency.

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