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MHT CET202410 May 2024Morning ShiftPhysicsAtomic PhysicsActual

Using Bohr's model, the orbital period of electron in hydrogen atom in n ^ th orbit is ( m = mass of electron, h = Planck's constant, e = electronic charge, ₀= permittivity of free space)

Options

  1. A2 ₀^2 n ^2 ~h ^2 me ^4
  2. B4 ₀^2 n ^2 ~h ^2 me ^2
  3. C4 ₀^2 n ^3 ~h ^3 m e ^4
  4. D4 ₀ n ^2 ~h ^2 me ^2

Correct answer

C. 4 ₀^2 n ^3 ~h ^3 m e ^4

Step-by-step solution

r = radius of n ^ th orbit = n ^2 ~h ^2 mZe ^2 v = speed of e ⁻ in n ^ th orbit = Ze ^2 2 ₀ n h T = 2 r v Substituting values of v and r , T = 4 ₀^2 n ^3 ~h ^3 m Z ^2 e ^4 For hydrogen, Z =1 T= 4 ₀^2 n ^3 ~h ^3 me ^4

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