Hydrogen part II
L = 0 there is only one state since it is a
sphere
l= 1 there are three states but it depends
on the orientation (superposition of 3 states)
L = 2 there are 5 states that get
superimposed
L = (2l + 1
You should make it complex
x=rsin#cos$
y=rsin#cos$
z= rcos#
Group-
things that you can do, combined you get a rotation (5 + 10 = 15 degrees)
Rotations
don’t commute
One
rotation times the second isnt always the same depending on the order
1925.
Electron spin
Found
the 2 state
Can
be spin up or spin down
If
it is spin up, then there is a probability for it to be spin up or spin down
Pauli
would rock on his chair so the experiments don’t work
The
Pauli affect
1926.
Wave functions
L
= 0 and spin 1/2
(1/2
because you want to get the even numbers for l)
Electron
in orbit has a magnetic moment proportional to l and the spin
So
its related to the angular momentum
Classical
vs. quantum for angular momentum
L
= 0 X spin 1/2 = 1/2
L
= 1 X spin 1/2 = 6 states but only two of them linearly combine
=
split into 2 states and four states
1/2
+ 3/2
L
= 2 X spin 1/2 = 3/2 + 5/2
1932.
Neutron was found
1936.
Nuclear fission
They
didn’t go any farther in atomic level because we had the Dirac theory
But
anytime you squared the field it would be infinity
It
was found through experiment that 2s 1/2 was less energy than 2p 1/2
They
are separated by 1057 MHz and this is called the Lamb shift
This
went against Dirac's theory that they were equal
1947.
Relativistic equations were made in
America but also in Japan
21
cm line
The
proton also spins
Learn
about structure of galaxy
So
the electron can be spin up or down
The
proton can be spin up or down too