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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

(1.6×1019)5(9.1×1031)(3.14)2×(0.53×1010)22×(8.85×1012)2×(6.63×1034)×12

3.73×1010C/kg.


Physics
Concepts of Physics
Standard XII

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