Physical Principles of Electron Microscopy: An Introduction to TEM ...

Analytical Electron Microscopy 157
An appealing feature of the Bohr model is that it provides an explanation
of the photon-emission and photon-absorption spectra of hydrogen, in terms
of electron transitions between allowed orbits or energy levels. When excess
energy is imparted to a gas (e.g., by passing an electrical current, as in a lowpressure
discharge), each atom can absorb only a quantized amount of
energy, sufficient to excite its electron to an orbit of higher quantum number.
In the de-excitation process, the atom loses energy and emits a photon of
well-defined energy hf given by:
hf = �R Z 2 /nu 2 � (�R Z 2 /nl 2 ) = RZ 2 (1/nl 2 � 1/nu 2 ) (6.5)
where nu and nl are the quantum numbers of the upper and lower energy
levels involved in the electron transition; see Fig. 6-1. Equation (6.5)
predicts rather accurately the photon energies of the bright lines in the
photoemission spectra of hydrogen (Z = 1); nl = 1 corresponds to the Lyman
series in the ultraviolet region, nl = 2 to the Balmer series in the visible
region, and so forth. Equation (6.5) also gives the energies of the dark
(Fraunhofer) lines that result when white light is selectively absorbed by
hydrogen gas, as when radiation generated in the interior of the sun passes
through its outer atmosphere.
Unfortunately, Eq. (6.5) is not accurate for elements other than hydrogen,
as Eq. (6.1) does not take into account electrostatic interaction (repulsion)
between the electrons that orbit the nucleus. To illustrate the importance of
this interaction, Table 6-1 lists the ionization energy (�E1) of the lowestenergy
(n = 1) electron in several elements, as calculated from Eq. (6.4) and
as determined experimentally, from spectroscopy measurements.
Table 6-1. K-shell (n = 1) ionization energies for several elements, expressed in eV.
Element Z �E1 (Bohr) �E1 (measured)
H 1 13.6 13.6
He 2 54.4 24.6
Li 3 122 54.4
C 6 490 285
Al 13 2298 1560
Cu 29 11,440 8979
Au 79 84,880 80,729