MHT CET202122 Sep 2021Morning ShiftPhysicsMagnetic Effects of CurrentActual
Assuming the atom is in the ground state, the expression for the magnetic field at a point nucleus in hydrogen atom due to circular motion of electron is [ ₀= . permeability of free space, m= mass of electron, ₀= permittivity of free space, h = Planck's constant]
Options
- A₀ e ^7 m ^2 8 ₀^3 ~h ^5
- B₀ e ^5 ^2 ~m ^2 8 ₀^2 ~h ^4
- C₀ e ^5 m ^3 8 ₀^3 ~h ^5
- D₀ e ^7 ^2 ~m ^2 8 ₀^3 ~h ^5
Correct answer
A. ₀ e ^7 m ^2 8 ₀^3 ~h ^5
Step-by-step solution
The magnetic field at the center of a circular coil is given by B = ₀ I 2 r If T is the periodic time of revolving electron, then I = e T Also, T = 2 r V I = eV 2 r B = ₀ eV 4 r ^2 For electron in ground state, V = e ^2 2 ₀ ~h and r = h ^2 ₀ m ^2 Putting these values in eq.(1) and simplifying we get B = ₀ e ^7 m ^2 8 ₀^3 ~h ^5