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MHT CET 202622 AprilEvening Shift
Exam
MHT CET
Year
2026
Date
22 April
Shift
Evening Shift
Subject
Physics
Chapter
Atomic Physics

MHT CET 2026 · 22 April · Evening Shift · Physics · Atomic Physics

The ratio between the areas of Bohr's first three orbits of the...

The ratio between the areas of Bohr's first three orbits of the hydrogen atom are

Options

  1. A1:16:811 : 16 : 81
  2. B1:8:271 : 8 : 27
  3. C1:4:91 : 4 : 9
  4. D1:2:31 : 2 : 3

Correct answer

A. 1:16:811 : 16 : 81

Step-by-step solution

The radius of the nn-th Bohr orbit is given by rn∝n2r_n \propto n^2.

The area of the orbit is An=πrn2A_n = \pi r_n^2.

Substituting the proportionality of the radius, we get An∝(n2)2⇒An∝n4A_n \propto (n^2)^2 \Rightarrow A_n \propto n^4.

For the first three orbits, n=1,2,3n = 1, 2, 3.

The ratio of their areas is A1:A2:A3=14:24:34=1:16:81A_1 : A_2 : A_3 = 1^4 : 2^4 : 3^4 = 1 : 16 : 81.

Answer: 1:16:811 : 16 : 81
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