230
5 Atomic Systems
with the · · · allowing for electronic terms associated with excited electronic
configurations (all lying at considerably higher energies than the 3 P 0 term of the
ground configuration that we have considered thus far). Note that we have also
set e
0 = 0 for the ground energy because an arbitrary shift in the zero of energy
affects neither the probabilities for occupation of an energy level nor any of the
thermodynamic quantities with which we shall be concerned.
In addition, we note that even the 1 D 2 term associated with the ground electronic
configuration contributes very little to z el (T ) for temperatures below 2000 K. It
contributes only 0.66% for T = 2000 K, while the 3 P 0 , 3 P 1 , and 3 P 2 levels contribute
12.33%, 35.01%, and 51.94%, respectively, to z el (T = 2000 K).
Note that for monatomic species the main concern is with low-lying excited
electronic states, such as those found in the 3 P 1 and 3 P 2 levels of the groundconfiguration Si atom. When an atom is in one of these excited electronic states,
the energy of the atom is given as
= tr + el ,
(5.3.6)
and the corresponding form for the atomic partition function is given by the product
z(T , V ) = z tr (T , V )z el (T ).
(5.3.7)
5.3.3 Nuclear Spin Contributions to the Canonical Partition
Function
The excitation energies associated with excited nuclear states of an atom are very
large indeed (typically of order MeV), which means that the nuclear degrees of
freedom can be considered to be unexcited, and play a role in the determination
of the partition function only in the case that the ground state of a nucleus is
degenerate (which typically means that the nucleus has a nonzero nuclear spin I ).
The nuclear partition function has precisely the same form as that developed above
for the electronic partition function, i.e.,
z nuc (T ) = e
−ββ n
0
ω
n
0 + ω
n
1 e
−βββ n
1 + ω
n
2 e
−βββ n
2 + · · ·
,
(5.3.8)
with the difference being that n
i is typically many orders of magnitude greater
than the thermal energy k B T , so that z nuc (T ) reduces to
z nuc (T ) = ω
n
0 e
−ββ n
0 ,
(5.3.9)
which, with n
0 ≡ 0 chosen for the nuclear ground state energy, becomes simply
5 Atomic Systems
with the · · · allowing for electronic terms associated with excited electronic
configurations (all lying at considerably higher energies than the 3 P 0 term of the
ground configuration that we have considered thus far). Note that we have also
set e
0 = 0 for the ground energy because an arbitrary shift in the zero of energy
affects neither the probabilities for occupation of an energy level nor any of the
thermodynamic quantities with which we shall be concerned.
In addition, we note that even the 1 D 2 term associated with the ground electronic
configuration contributes very little to z el (T ) for temperatures below 2000 K. It
contributes only 0.66% for T = 2000 K, while the 3 P 0 , 3 P 1 , and 3 P 2 levels contribute
12.33%, 35.01%, and 51.94%, respectively, to z el (T = 2000 K).
Note that for monatomic species the main concern is with low-lying excited
electronic states, such as those found in the 3 P 1 and 3 P 2 levels of the groundconfiguration Si atom. When an atom is in one of these excited electronic states,
the energy of the atom is given as
= tr + el ,
(5.3.6)
and the corresponding form for the atomic partition function is given by the product
z(T , V ) = z tr (T , V )z el (T ).
(5.3.7)
5.3.3 Nuclear Spin Contributions to the Canonical Partition
Function
The excitation energies associated with excited nuclear states of an atom are very
large indeed (typically of order MeV), which means that the nuclear degrees of
freedom can be considered to be unexcited, and play a role in the determination
of the partition function only in the case that the ground state of a nucleus is
degenerate (which typically means that the nucleus has a nonzero nuclear spin I ).
The nuclear partition function has precisely the same form as that developed above
for the electronic partition function, i.e.,
z nuc (T ) = e
−ββ n
0
ω
n
0 + ω
n
1 e
−βββ n
1 + ω
n
2 e
−βββ n
2 + · · ·
,
(5.3.8)
with the difference being that n
i is typically many orders of magnitude greater
than the thermal energy k B T , so that z nuc (T ) reduces to
z nuc (T ) = ω
n
0 e
−ββ n
0 ,
(5.3.9)
which, with n
0 ≡ 0 chosen for the nuclear ground state energy, becomes simply