Question

In a hydrogen atom the electron moves in an orbit of radius 0.5 A_o making 10 revolutions per second, the magnetic moment associated with the orbital motion of the electron will be

(i) 2.512 x 10^-38 Am²

(ii) 1.256 x 10^-38 Am²

(iii) 0.628 X10^-38 Am²

(iv) zero

Answer 1

Answer is (ii) 1.256 x 10^-38 Am²

R = 0.5 A°

ω = 10 rps = 10 × 2π rad/s

v = 10 Hz

M = I A = evπ r²

= 1.6 × 10^–19 × 10 × 3.14 × 0.5 × 0.5 × 10^–10 × 10^–10

= 1.256 × 10^–38 Am²