The Bohr Magnetron
We can picture an electron in an atom moving in a circle of radiuswith speed
The moving electron is equivalent to a current loop. A current loop with areaand currenthas a magnetic dipole moment given byso for the electron aboveTo find the current associated with the electron, notice that the time for one orbit isso the current associated with the electron,
The magnetic momentis then
We can expressin terms of the angular momentumof the electron.
For electrons in atoms, angular momentum is quantized. It's component in a particular direction is an integral multiple ofIfthen
is called the Bohr magneton and denotedIt's numerical value is