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 [ array l ₀ permeability of free space, m mass of electron ₀ permittivity of free space, h Planck's constant array ]

Step-by-step solution

To keep the electron in its orbit, the centripetal force on the electron must be equal to the electrostatic force of attraction, According to Bohr's angular momentum quantization condition: r m e^2= ₀ h^2r= ₀ h^2 m e^2 ---(3) From (ii) and (iii), we have v= h m e^2 2 m ₀ h^2 = e^2 2 ₀ h The magnetic field at the center of the circular loop is given by, B= ₀ I 2 r where, current I= q T and time T= 2 r v I= e v 2 r Using, equations (2), (3) and (4) we have, B= ₀ e^7 m^2 8 ₀^3 h^5