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MHT CET202615 April 2026Evening ShiftPhysicsAtomic PhysicsActual

In the hydrogen atom, radii of the first four Bohr orbits are related as

Options

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

Correct answer

C. 1 : 4 : 9 : 16

Step-by-step solution

The radius of the n -th Bohr orbit in a hydrogen-like atom is given by r_n = n^2 h^2 ₀ m e^2 Z . For a hydrogen atom, Z = 1 , which implies r_n n^2 . For the first four orbits, n = 1, 2, 3, 4 . The ratio of their radii is r₁ : r₂ : r₃ : r₄ = 1^2 : 2^2 : 3^2 : 4^2 = 1 : 4 : 9 : 16 . Answer: 1 : 4 : 9 : 16

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