MHT CET202310 May 2023Evening ShiftPhysicsAtomic PhysicsActual
What is the moment of inertia of the electron moving in second Bohr orbit of hydrogen atom? [ h = Planck's constant, m = mass of electron, ₀= permittivity of free space, e = charge on electron]
Options
- A4 ₀^2 h^4 ^2 m e^4
- B8 m ₀^2 h^4 ^2 e^4
- C16 ₀^2 h^4 ^2 m e^4
- D₀^2 h^4 16 ^2 m e^4
Correct answer
C. 16 ₀^2 h^4 ^2 m e^4
Step-by-step solution
Moment of Inertia I = MR ^2 Radius of the n ^ th Bohr orbit is, r_n= ₀ h^2 n^2 me ^2 For n =2 , r₂= 4 ₀ h^2 m e^2 Moment of inertia of the electron in the 2^ nd orbit is aligned M.I & = m [ 4 ₀ ~h ^2 me ^2 ]^2 & = m 16 ₀^2 ~h ^4 ^2 ~m ^2 e ^4 & = 16 ₀^2 ~h ^4 ^2 me ^4 aligned