Q26 of 106 Page 384

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.

We know that magnetic dipole moment is


And we know that


Adding both the equations we get



Hence,


Now from Bohr’s model



And area is equal to


So,


Now, angular momentum


Now




Since this term is independent of Z so it is universal constant.


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