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MHT CET Medical202622 April 2026Evening ShiftPhysicsAtomic PhysicsActual

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

Options

  1. A1 : 16 : 81
  2. B1 : 8 : 27
  3. C1 : 4 : 9
  4. D1 : 2 : 3

Correct answer

A. 1 : 16 : 81

Step-by-step solution

The radius of the n -th Bohr orbit is given by r_n n^2 . The area of the orbit is A_n = r_n^2 . Substituting the proportionality of the radius, we get A_n (n^2)^2 A_n n^4 . For the first three orbits, n = 1, 2, 3 . The ratio of their areas is A₁ : A₂ : A₃ = 1^4 : 2^4 : 3^4 = 1 : 16 : 81 . Answer: 1 : 16 : 81

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