Spectra
We X-Ray have seen that hydrogen emission lines come in groups, and that the shortest
wavelengths of light it can produce fall in the UV portion of the spectrum. Clearly, x-ray
wavelengths would have to come from other atoms. In fact, the Rydberg equation can be
adjusted so that it approximates the emission spectra of heavier elements if we divide by
the square of the atomic number, Z, which is simply the elements number on the
periodic table: = R n n' / ( n n' )Z, where the Rydberg wavelength is still 91.1nm.
Recognizing that the shortest wavelengths are produced when n'=1 and n=, it follows
that to get a wavelength around 100pm, Z must be at least 20. Transition metals are ideal
candidates for this. The caveat to using the modified Rydberg equation is that the
atom in question must be missing all but one electron. Otherwise, it is not enough like
hydrogen to yield any accuracy. Still, it was found that when metal targets were
bombarded by cathode raysbeams of fast electronsx rays emissions were the result.
A notation often employed for specifying spectral emission lines due to electron deexcitation uses the shell letter in which the in-falling electron ends up. Recall that the n=1
level is also called the K shell and the higher shells follow alphabetically with the
subsequent capital letters. Depending on how many levels by which the electron drops to
emit the photon, the shell letter receives a subscripted Greek letter where stands for 1,
is 2, is 3, et cetera. Suppose, for instance, that a photon is emitted from an atom when
an excited electron drops from the n=6 shell to the n=2 shell. It therefore up ends in the L
shell, and it dropped 4 levels. The fourth letter of the Greek alphabet is delta (), so the
line is labeled L . If this atom were hydrogen, this would be called the fourth Balmer line.
When the source of the excitation is a cathode ray, many of the beams electrons will
release random photons simply by slowing down upon impact with the atoms of the
target. This produces a blackbody-like spectral curve known by the German word for
braking radiation: bremsstrahlung. The shortest frequency for the bremsstrahlung
spectrum results from all of the impacting electrons energy being converted to a photon,
so this cutoff wavelength can be found using Plancks law: c = hc/E where E is the
energy of the electrons in the beam. This energy is very often measured in electron volts
(eV) since it consists of electrons being accelerated through a set voltage. One eV is
1.60210-19J. Notice that this same number is the charge of the electron measured in
coulombs. That is not a coincidence. The point is that since electron volts and nanometers
are used so often in atomic and nuclear physics, it is useful to know hc = 1240eVnm.
This will save you the time of plugging h and c in separately and converting the units.
Superposed atop the bremsstrahlung spectrum is a
characteristic spectrum of the material in the target. This
consists of bright lines (narrow, tall peaks in intensity) that
can distinctly identify the element involved. The only
difference between these lines and the ones produced by
electrical or thermal excitation is that these come from inner
shells, while the other always come from the outer shell.
c