with
speed
University Physics Notes: Quantum Mechanics – The Bohr Magneton
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 area
and
current
has
a magnetic dipole moment given by
so
for the electron above
To
find the current associated with the electron, notice that the time
for one orbit is
so
the current associated with the electron,
The magnetic moment
is
then
We can express
in
terms of the angular momentum
of
the electron.
For electrons in atoms, angular momentum is quantized. It's
component in a particular direction is an integral multiple
of
If
then
is
called the Bohr magneton and denoted
It's
numerical value is