Thermal X-ray radiation (PDF) - SRON

• The first atomic shell (n = 1) has l = 0, and there are two possible orientations
of the spin ⃗s, hence there are two 1s orbits. If there is one electron in this
shell, the designation is 1s. If the shell is full, with two electrons, we write 1s 2
for a closed shell.
• The second shell (n = 2) has as one particular possibility l = 0, s = ±1/2,
and these orbits are called 2s orbits. But however for n = 2 we also can have
l = 1.
• For l = 1, the orbital angular momentum can have three orientations, given
by m l = −1, 0, 1, and again the electron spins can have two different values,
s = ±1/2. This then leads to 6 different p-orbits, and since n = 2, these are
2p orbits. The full n = 2 shell is now designated as 1s 2 2s 2 2p 6 . Frequently one
omits the filled shells, so that for example 1s 2 2s 2 2p 5 is abbreviated as simply
2p 5 .
• The third closed shell is 1s 2 2s 2 2p 6 3s 2 3p 6 3d 10 , etc. There are 10 d-orbits
because there we have l = 2 and hence m l = −2, −1, 0, 1, 2 which can be
combined with two different electron spin values.
• The sequence of filling subshells obeys the following rules: first fill orbits in
order of increasing n + l, and where n + l has the same value, fill the orbits
in order of increasing n. Therefore, the order of filling is 1s, 2s, 2p, 3s, 3p, 4s,
3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, . . .. The 4f orbit is an inner orbit, that is
filled only at relatively high nuclear charge (the rare earth elements).
A closed shell has no net contribution to the angular momentum:
∑
⃗l i = 0
i
∑
⃗s i = 0
i
∑
⃗j i = 0
i
∑
l i = even
i
∑
s i = integer.
Each given electron configuration corresponds to a certain group of terms which
all have approximately similar energies (see also §3.4.3).
3.2.4 Term notation
In general, a term with quantum numbers LSJ is designated as r (L-symbol) J . We
can illustrate this with an example.
Example 3.5. Take the electron configuration 1s 2 2s 2 2p 6 3s 2 3p 2 , with L = 1,
S = 1, J = 2. This is designated as 1s 2 2s 2 2p 6 3s 2 3p 2 3 P 2 , or shortly with omission
of the closed shells, as 3p 2 3 P 2 (pronounce as ”three p two triplet p two”). This is
a triplet term.
In general we omit all shells from the designation that are spectroscopically
irrelevant. Whenever the algebraic sum ∑ l i = even or odd, the term is even or
i
odd. For example, the doublet term 2 D is even, while the triplet term 3 P o is odd.
Therefore sometimes the index o from ”odd” is added just like in the triplet P term
above. In the table below we give as examples the ground state configuration of a
few atoms.
i
10