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.

Question

Philoid · Accepted Answer

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.