Question

# Show that the ratio of the magnetic dipole moment  to the angular momentum (l = mvr) is a universal constant for hydrogen-like atoms and ions. Find its value.

Solution

## Magnetic dipole moment = ni A =  e×mc2×πr22n22e.h3n3 Angular momentum = mvr =  nh2π Since the ratio of magnetic dipole moment, and angular momentum is independent  of 'Z'. Hence it is a universal constant Ratio =  e5×m×πr2 n224 ϵ0h3n3×2πnh (1.6×10−19)5(9.1×10−31)(3.14)2×(0.53×10−10)22×(8.85×10−12)2×(6.63×10−34)×12 =  3.73×1010C/kg. PhysicsConcepts of PhysicsStandard XII

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