An applied magnetic field splits the energy level of an electronic
orbital,
m=
e(h/2p)
2me
æ è
L
(h/2p)
ö ø
, dE=-m ·B =
e(h/2p)
2me
m Bz = mB m B ,
where the Bohr magneton is defined as
aB º [(e(h/2p))/(2me)] .
It is interesting to calcultate the Bohr magneton from some essential
atomic numbers without really going into SI units.
Letus calculate the dipole energy of m=1 due to an magnetic field of
strngth 1 T.
dE =
e(h/2p)
2 me
(1 Tesla ) =
(h/2p) c
2 me c2
e c (1 Tesla )
=
1240 nm·eV/(2p)
2×511000 eV
e (3×108) ( m/s )·( Tesla )
= e
1240/6.2832
2×511000
×3×108×( 10-9meter ) · Volt/meter = 5.79×10-5eV
The above calculation is similar to the induced emf of a length of compton
wavelength moving at the speed of light under external magnetic field.
aB º
e(h/2p)
2 me
=5.79×10-5eV/T
The wavelength of photon emitted between the split levels
when the system is embedded at B=1 Tesla is
l =
hc
dE
=
1240
5.79×10-5
nm = 21,400,000 nm = 21.4 mm .
File translated from
TEX
by
TTH,
version 3.02. On 19 Mar 2008, 12:04.