Click
here or on the periodic table at the bottom ofthis document to view the x-ray spectra of 63 elements.
Viewing the Periodic Table of the Elements with X-rays
Gregory Rech1,2, Jeffrey Lee1,3, Eric B. Norman1, Ruth-Mary Larimer1, and Laura Guthrie1,4
1Lawrence Berkeley National Laboratory, Berkeley, CA
2
University of California, Berkeley, CA3
University of California, Irvine, CA4
Acalanes High School, Lafayette, CAHistory
X-rays and x-ray fluorescence are not new subjects to the field of physics. Wilhelm Röntgen discovered x-rays in 18951, and in 1901 he was awarded the very first Nobel Prize in physics for this discovery2. Soon after, Charles Glover Barkla discovered that each element has its own characteristic x-ray spectrum2. He was awarded a Nobel Prize in physics for this discovery in 19172. Sir William Henry Bragg and his son, Sir William Lawrence Bragg, were then able to experimentally prove that the discrete electron energy levels of an atom, an idea proposed by Niels Bohr, actually existed2. They were awarded the Nobel Prize in physics for this in 19152. After this groundwork in x-ray spectroscopy was established, Henry Moseley showed that each element’s characteristic x-ray energy spectrum followed the predictions of the Bohr atomic model1. He developed a graphical method to display this data, now known as the Moseley diagram, which is displayed in Figure 1. This diagram was the first way that scientists were able to definitively establish the atomic numbers of the elements1.
Figure 1
– The Moseley diagram as first published by Moseley3. It displays alinear relationship between an atom’s atomic number and the square root of the
frequency of its atomic x-rays.
The Physics of x-rays
X-rays are high-energy photons that are produced when electrons make transitions from one atomic orbit to another. These transitions can be generated via the photoelectric effect as illustrated in Figure 2. If you send a photon into an atom with an energy greater than the binding energy of an electron in that atom, the photon can knock that electron out of its orbit, leaving a hole (or vacancy). This hole can then be filled by another electron in the atom, giving off an x-ray in the transition to conserve energy. This process is known as fluorescence. Many different atomic electrons of different binding energies can fill this hole, so you would expect to see many energy peaks in an x-ray spectrum.
Figure 2 - A pictorial representation of x-ray fluorescence using a
generic atom and generic energy levels. This picture uses the Bohr
model of atomic structure and is not to scale.
Notation
The allowed energies of electrons in atoms are discrete. These energies depend on three quantum numbers, called n, l and j. n, the principle quantum number, is an integer having values of 1,2,3…. l, the orbital angular quantum number, is an integer having values of 0,1,…, n-1. j is the total angular momentum of an energy level and is equal to l + 1/2. Barkla assigned the letter K to electrons in the n = 1 shell, L to electrons in the n = 2 shell, and so on1. Electron transitions to the K shell of an atom are called K x-rays, and transitions to the L shell are called L x-rays. This historical nomenclature is still in use today. An analog to this particular nomenclature exists in chemistry and may be more familiar. In chemistry, values of n start at 1 and increase in successive integers, whereas values of l are denoted by the letters s, p, d, f, g and so on. In this paper, we will use Barkla’s system.
Not only are energy levels labeled, but specific atomic transitions are labeled also. Some of these labels are displayed in Figure 3 below. The K
a1 x-ray is emitted in a transition from the n = 2, j = 3/2 level to the K-shell; the Ka2 x-ray is emitted in a transition from the n = 2, j = 1/2 level to the K-shell.The K’
b1 transition is a combination of all the transitions from the M shell to the K shell and the K’b2 transition is a combination of all the transitions from the N shell to the K shell.
Figure 3
– A diagram displaying the nomenclature of the allowed energy levels andthe allowed electron transitions of a generic atom. The red circles represent electrons.
The number of electrons in each energy level is 2j + 1. Energy is increasing in the
direction of increasing n, and the energy levels are not to scale.
The Experiment
Figure 4
– Greg Rech standing next to the experimental setup.
The project we undertook was designed to help students understand atomic processes. We produced a total of 63 energy spectra of individual elements plus 12 spectra of "unknown" samples that students can analyze in order to determine their elemental compositions.* Students can also send in an "unknown" sample to be fluoresced, get back the x-ray spectrum of the "unknown" sample, compare it to the standards on the web, and then determine which elements are in their "unknown" sample. We hope that this will provide a useful visual aid for students and teachers to go along with the abstract concepts found in atomic science.
In order for us to fluoresce many different elements, we needed a radioactive source that produced a gamma ray (a high-energy photon produced by a nuclear transition) with an energy higher than the binding energy of the K electrons of these elements. We ended up using an 241Am source, which decays by the following process: 241Am à 237Np + 4He
+ 5.6 MeV4. The 237Np nucleus then decays into a lower energy state by emitting a 59.537 keV gamma ray4, which we used to fluoresce the elements. With this gamma ray we were able to fluoresce the K electrons of the elements ranging from Ca (atomic number, Z, = 20), whose K electron has a binding energy of 4.038 keV, to Tm (Z = 69), whose K electron has a binding energy of 59.390 keV. For elements with Z ranging from 70 (ytterbium) to 83 (bismuth), we were able to fluoresce only the L shell electrons. All of the elements with Z > 83 are radioactive. To avoid the complications that arise from radioactive samples, we chose to fluoresce only uranium and thorium, since they have reasonably high natural abundances and low levels of radioactivity.To measure the x-rays emitted from each target, we used a planar germanium detector 1.3 cm thick and 3.6 cm in diameter sitting at a 90o angle from the 241Am source, as shown in Figure 5. We irradiated the sample with the 59.537 keV gamma rays, resulting in many of the fluoresced x-rays to be emitted towards the detector. We acquired the x-ray spectra in 512 channels using an ORTEC, PC based data acquisition system.
Figure 5
– A picture of the experimental setup. The 241Am source is the small diskat the end of the rod coming out of the cylinder in the bottom right-hand corner of
the picture. The spool of solder is the sample in this case, and contains indium.
The germanium detector is sitting inside the long cylinder that is attached to the big thermos
bottle filled with liquid nitrogen.
The Spectra
The energy spectrum shown in Figure 6 of germanium is a good example of one of our fluoresced elements with a low atomic number. You can see two x-ray energy peaks caused by electron transitions to its K shell. Our detector’s resolution was not good enough to distinguish between the different K
a and Kb x-rays for germanium, so the two peaks that you see are a mixture of all the Ka x-rays and all the Kb x-rays with the Ka mixture being the peak with the lowest energy. The L x-rays of germanium are too low in energy to be seen in this spectrum.
Figure 6 - An x-ray spectrum of germanium (Z = 32) showing its characteristic
K x-ray energy peaks.
Figure 7 displays the x-ray spectrum of erbium, one of our high Z elements. You can see several high-energy peaks caused by electron transitions to its K shell. The energy levels of erbium are spread far enough apart so that our detector could resolve specific electron transitions as opposed to germanium where the two peaks were mixtures of electron transitions. Using Figure 3, the shape of this x-ray spectrum can be qualitatively explained. In the spectrum you can see that the K
a1 peak has about twice as many counts in it as the Ka2 peak. In the generic energy level diagram you can see that there are twice as many electrons, represented as red circles, available for the Ka1 transition as there are for the Ka2 transition. If you assume that the probability of an atomic transition is only dependent on the number of available electrons and on the separation of energy levels, then it makes sense that there are twice as many counts in the Ka1 peak as the Ka2 peak. The separation of the energy levels within the L shell is much smaller than the separation of the energy levels of the L shell and those of the K shell. That makes the energy of the Ka1 transition about equal to the energy of the Ka2 transition, which means that, in this case, the probability for a transition to occur is solely based on the number of electrons in the energy levels in question.These are just two examples of the x-ray spectra that we have already put on this web site. We hope that this site will be a useful tool for students and teachers alike to become more familiar with atomic processes.
Figure 7 - An x-ray spectrum of erbium (Z = 68) showing both K and L x-rays.
Notice that the L x-rays have lower energy than the K x-rays due to the fact that the
allowed electron levels of an atom get closer together in energy as n increases.
If you would like to learn more about radioactive decay or neutron activation anlaysis, please visit our other websites: http://ie.lbl.gov/gamma and http://ie.lbl.gov/naa
* Please contact Eric Norman at
EBNorman@lbl.gov to get the composition of the "unknown" samples.This work was supported by the U. S. Department of Energy contract No. DE-AC03-76SF00098.
References
The Data
Figure 8
– This is our version of the periodic table of the elements with 63of its spaces filled by the elements that we fluoresced.