Biomedical Engineering Reference
In-Depth Information
Table 14.1
Some electronic states for helium
State
Spatial part
Spin part
Energy,
ε
1
√
2
(α(
s
1
)β(
s
2
)
−
α(
s
2
)β(
s
1
))
Ψ
1
1
s
(
r
1
)
1
s
(
r
2
)
2
ε
1
s
1
√
2
(
1
s
(
r
1
)
2
s
(
r
2
)
1
√
2
(α(
s
1
)β(
s
2
)
Ψ
2
+
1
s
(
r
2
)
2
s
(
r
1
))
−
α(
s
2
)β(
s
1
))
ε
1
s
+
ε
2
s
Ψ
3
α(
s
1
)α(
s
2
)
ε
1
s
+
ε
2
s
1
√
2
(
1
s
(
r
1
)
2
s
(
r
2
)
−
1
√
2
(α(
s
1
)β(
s
2
)
+
α(
s
2
)β(
s
1
))
Ψ
4
1
s
(
r
2
)
2
s
(
r
1
))
ε
1
s
+
ε
2
s
Ψ
5
β(
s
1
)β(
s
2
)
ε
1
s
+
ε
2
s
1
√
2
(α(
s
1
)β(
s
2
)
−
α(
s
2
)β(
s
1
))
Ψ
6
2
s
(
r
1
)
2
s
(
r
2
)
2
ε
2
s
above the ground state. Since
Z
2 for heliumwe calculate awavenumber of 329 212 cm
−
1
.
Experimental data can be found at the NBS/NIST website http://www.nist.gov as given in
Table 14.2.
=
Table 14.2
Experimental data for helium
Configuration
Term
J
Term value/cm
−1
1s
2
1
S
0
0
1s
1
2s
1
3
S
1
159 856.07760
1s
1
2s
1
1
S
0
166 277.542
I should explain that the
J
quantum number is similar to the
j
quantum number we
met in our study of one-electron atoms in Chapter 13; for light atoms such as helium
it is determined by combining together the individual electron orbital and spin angular
momentum quantum numbers, according to a set of well-known rules called the
Russell-
Saunders
scheme. We combine together the
l
quantum numbers for the two electrons;
since
l
0 for an s electron, the allowed resultant
L
is also 0. The electronic states are
therefore S states. We also combine together the spin quantum numbers
s
. Since
s
=
=
1
/
2
for an electron, the allowed values of the resultant
S
are
1
/
2
+
1
/
2
and
1
/
2
−
1
/
2
and the spin
multiplicities 2
S
+
1 are 1 and 3. We then combine the
L
's and the
S
's in the same way
to get
J
.
The zero-order model is not even qualitatively correct; it overestimates the energy dif-
ference between the ground state and the excited states, and has nothing at all to say about
the experimentally interesting difference between the singlet and the triplet excited states.
This poor agreement with experiment is mostly due to our neglect of electron repulsion
but is in part due to the fact that each electron shields the other electron from the Coulomb
attraction due to the nucleus.
