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MHT CET202210 Aug 2022Evening ShiftPhysicsAtomic PhysicsActual

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

Options

  1. A4 ₀^2 n^3 h^3 m e^4
  2. B4 ₀^2 n^2 h^3 m e^3
  3. C4 ₀ n h^3 m e^2
  4. D4 ₀ n^2 h^2 m e^2

Correct answer

A. 4 ₀^2 n^3 h^3 m e^4

Step-by-step solution

The orbital period of revolution of electron in n^ th orbit is T_n= 2 r_n v_n Bohr radius for n^ th orbit r_n= ( h^2 ₀ m e^2 ) n^2 Z and v_n= ( e^2 2 h ₀ ) Z n . T_n=2 h^2 ₀ n^2 m e^2 Z 2 h ₀ n e^2 Z = 4 ₀^2 n^3 h^3 m e^4 Z^2 For hydrogen atom, Z=1 T_n== 4 ₀^2 n^3 h^3 m e^4

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