Thermal X-ray radiation (PDF) - SRON

3.2 Summary of spectroscopic notations
3.2.1 Atoms or ions with one valence electron
The electrons in an atom have orbits with discrete energy levels and quantum numbers.
The valence electron or light-electron in an atom or charged ion is the electron
in the outermost atomic shell which is responsible for the emission of light. The
energy configuration can be described by four quantum numbers:
n - principal quantum number, characteristic for the relevant shell. It takes discrete
values n =1, 2, 3, . . .. An atomic shell consists of all electrons with the same
value of n.
l - quantum number of angular momentum of orbital motion of the electron: l =
0, 1, 2, . . . n − 1.
s - quantum number of spin of electron: s = ±1/2 (for l > 0) or s = 1/2 (for
l = 0).
j - quantum number of total angular momentum of electron: j = l±1/2 (for l > 0)
or j = 1/2 (for l = 0).
All angular momenta are measured in units of = h/2π (h is Planck’s constant).
The magnitude of the angular momentum vectors is given by
| ⃗ l| = √ l(l + 1) ≈ l (l ≫ 1).
Note that ⃗j = ⃗ l + ⃗s.
For hydrogenic orbits (Coulomb field) in the theory of Bohr, the semi-major
axis r of an elliptical orbit in shell n is given by r = n 2 a 0 /Z, where Z is the
nuclear charge and the Bohr radius a 0 equals 5.291772108 × 10 −11 m (∼0.529 Å).
Note that a 0 = α/4πR ∞ with α the fine structure constant and R ∞ the Rydberg
constant R ∞ = m e cα 2 /2h; R ∞ hc = 1 2 α2 m e c 2 is the Rydberg energy (13.6056923 eV,
2.17987209 × 10 −18 J). Thus, heavy nuclei are more compact, and also the orbits
with small n are more compact than orbits with large n.
The principal quantum number n corresponds to the energy I n of the orbit.
In the classical Bohr model for the hydrogen atom the energy I n = E H n −2 with
E H = 13.6 eV the Rydberg energy. Thus, electrons with large value of n have small
energies (and therefore are most easily lost from an atom by collisons).
Further, the characteristic velocity of the electron in the Bohr model is given
by v = αZc/n. Electrons withsmall n or in atoms with large Z have the highest
velocities. These velocities are sometimes useful to see if an interaction is important
or not. For instance, if a free electron or proton collides with an atom, it will have the
longest and most intense interaction with those electrons that have similar orbital
velocity as the velocity of the invader.
The following notation for electron orbits is frequently used:
l = 0 1 2 3 4 5 6 7 8 9
s p d f g h i k l m electrons
and further alphabetic (with no duplication of s and p, or course!). The characters
s, p, d and f originate from sharp, principal, diffuse and fundamental series (the line
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