An electron moves in Bohr orbit. The magnetic field at the centre is proportional to

Step-by-step solution

The magnetic field at the center of a Bohr orbit is determined by the electron's orbital motion. For hydrogen ( Z = 1 ), the velocity scales as v_n n⁻¹ and the orbital radius as r_n n^2 . The current generated by the orbiting electron is I = e v_n 2 r_n , which simplifies to I n⁻¹ n^2 = n⁻³ . The magnetic field at the center of a circular loop is B = ₀ I 2 r_n , yielding B n⁻³ n^2 = n⁻⁵ . B n⁻⁵