1. Basic Nuclear Physics - 2
Excitation, Ionisation, X-ray production and Auger electrons
Day 1- Lecture 2

2. Objective
To discuss the excitation and ionisation which are processes by which electrons are removed from their stable location
To learn about accelerated charged particles, x-rays, Bremsstrahlung, Characteristic X- rays and Auger electrons

3. Contents Binding Energy Excitation and Ionisation
Accelerated charged particles and x-rays
X- ray units
Bremsstrahlung
Characteristic Radiation
Auger electrons

4. Electron Shells
The electrons which travel around the nucleus of an atom are confined to discrete shells. In this figure, the shells are depicted as 2- dimensional orbits around the nucleus for simplicity, but in reality, the orbits are 3 dimensional and can be thought of as hollow shells. The electrons in a given shell are bound to the nucleus such that it requires a fixed amount of energy to free the electron from the nucleus. This amount of energy is referred to as the binding energy. Each shell is designated by a letter beginning with “K” assigned to the shell closest to the nucleus and continuing with “L”, “M”, “N” etc as the shells get larger or farther from the nucleus. Thus the “K” shell is the most tightly bound to the nucleus and consequently has the largest binding energy.

5. Maximum No. of Electrons
Electron Shells
Shell n
Maximum No. of Electrons K 1 2 L 8 M 3 18 N 4 32 O 5 50 P 6 72 K L M N O
The number of electrons that can exist in each shell is specified by the simple equation 2n2 where n represents the number of the shell. “K” being the innermost or smallest shell is designated as n=1 with “L” being designated as n=2 etc. Initially the shells are filled in order so that as the atomic number (Z) increases, the electrons appear in the lowest shell that can accommodate them. However, as the number of electrons increases, some may appear in higher shells even before the next lower one is completely filled. For example, potassium has 19 protons and 19 electrons. From the table above it would appear that potassium should have 2 electrons in the K shell, 8 in the L shell and 9 in the M shell. However, it actually only has 8 in the M shell and the last electron is in the N shell. As the atomic number increases, eventually, the M shell is filled with its full complement of 18 electrons.
In the case of Zirconium, one would assume that the electrons would be distributed as follows: K=2, L=8, M=18, N=12 for a total of 40. However, the N shell actually has only 10 instead of 12 and the remaining 2 electrons are in the O shell.
2n2

6. Binding Energy Shell Hydrogen Tungsten K -13.5 -69,500 L -3.4 -11,280M
-1.5
-2,810 N
-0.9
-588 O
-0.54
-73
As can be seen from the table, the binding energy for the K shell of hydrogen is 13.5 eV and the binding energy decreases as the shells become larger, decreasing to about 0.5 eV for the O shell. Similarly for tungsten, the K shell binding energy is 69.5 keV while the O shell binding energy is keV, a significant reduction. Since the binding energies represent the lack of freedom possessed by the electrons, they are designated here as negative energies where the higher the negative number the more tightly bound. To release the electron from the nucleus, positive energy equal to or greater than the binding energy must be imparted to the electron.
(Binding Energy in eV)

7. Binding Energy Binding Energy (keV) Atomic Number (Z) 110 100 90 80 7030 40 50 60 70
100 80 90
110 20
Atomic Number (Z)
Binding Energy (keV)
This graph indicates that the binding energy of the electrons increases as the atomic number (Z) increase. The excerpt from the table also shows that the binding energy of the K shell electrons designated as Kab increases as Z increases. From the table it is noted that between a Z value of 30 and 40 the binding energy increases from 10 to 18 keV which is also noted from the graph. The binding energy of the L shell electrons is much lower since they are in a higher and thus less tightly bound shell. From Z = 31 to 40, the L shell binding energy varies from 1.3 to 2.5 keV. Thus it can be inferred from the table that for Zirconium, to raise an electron from the K shell to the L shell (assuming there was a vacancy in the L shell) would require the transfer of about 15.5 keV to the K shell electron ( = keV).

8. Excitation atom excited state electron orbitals energy nucleus
ground state
energy
nucleus
atom
If energy is delivered to an electron, it can be induced to rise to a higher orbit which is less tightly bound to the nucleus. This is termed excitation. The electron is raised to an excited state while a vacancy appears in a more stable bound state. This is an unnatural situation. If an electron falls back into the vacant slot in the lower orbit, then radiation must be released.

9. Excitation higher energy level excited electron energy
normal energy level
higher energy level
excited
electron
energy
The electron is considered “excited” because it occupies an orbit which is less tightly bound and it left a vacancy in a more tightly bound orbit. It possesses excess energy compared to where it should be.

10. Excitation energy nucleus electron excited state
The energy needed to raise an electron to a higher orbit can originate from many sources such as charged particle interactions, photon interactions or particle collisions. Photon interactions will be discussed further in a separate lesson.

11. Excitation
A charged particle does not have to strike the electron to impart energy.
Simple electrostatic attraction or repulsion (depending on whether the particle is positively or negatively charged) can be sufficient to induce the electron to change its orbit provided enough energy is transferred.

12. Ionisation of an outer shell electron
A charged particle (+ or -) attracts or repels the orbital electron so that it leaves its orbit. Alternatively, a neutral particle such as a neutron must strike an electron to eject it from the atom. Even a massless photon with sufficient energy to free the electron from the atom can transfer its energy to the electron. The result of all these interactions is an ionisation event which creates two charged particles: the liberated electron and the residual atom now positive since it is missing one electron and thus has one unpaired proton.

13. Ionisation of a K-shell electron
The electron ejected from the atom need not be one from the highest (loosely bound) orbit or shell. Even the most tightly bound electrons, those in the K-shell can be ejected during the ionisation process. In order to ionise such an electron, the incoming radiation must possess an amount of energy at least equal to the binding energy of the electron. If the incoming radiation possessed only an amount of energy equal to the binding energy of the electron, the electron would be freed from the atom but would have no excess kinetic energy to travel away from the atom. It would remain in the immediate vicinity and would likely be recaptured by the outermost orbit if a vacancy existed there.
If however the incoming radiation possesses energy greater than the binding energy of the electron, then the excess energy (indicated in the graphic as E) is merely the initial energy of the incoming radiation (E) minus the energy expended to overcome the binding energy of the electron (Eo). This excess energy E is given to the freed electron as kinetic energy which permits it to travel far from the atom from which it originated. This will ultimately be the source of radiation dose which will be discussed in future modules.
The energy of a photon is proportional to its frequency: E = hf =hc/ , where h is Planck's constant = 6.63 x 10‑34 j·s, f is the frequency of the photon (s-1), c is the speed of light and  is the wavelength of the photon.

14. Accelerated Particles
A charged particle can be accelerated by subjecting it to a potential difference such as might be created by a simple battery. One terminal of the battery would be positive while the other negative. Positively charged particles would be attracted to the negative terminal and similarly, negatively charged particles would be attracted to the positive terminal. The strength of the battery (voltage) would determine how fast the particles are accelerated across the gap between the terminals.
More information concerning devices used to accelerate particles will be presented in a future lesson.

15. Bremsstrahlung
In one process radiation is emitted by the high-speed electrons themselves as they are slowed or even stopped in passing near the positively charged nuclei of the anode material. This radiation is often called Brehmsstrahlung [Ger.,=braking radiation].
The German word Bremsstrahlung translates as “braking radiation”. This implies that radiation is produced as a result of “braking” or deceleration or slowing down of charged particles. Charged particles which possess kinetic energy, travel at some velocity. If that velocity is decreased, some kinetic energy is lost. This lost energy can take many forms, one of which is x-radiation. Another common form of the lost energy is heat which of course is a form of energy.
Pictured in this image is an electron which has been deflected by passage near the large positively charged nucleus of a tungsten atom (Z = 74). The process of changing direction results in a loss of energy which in this case is emitted as an x-ray photon.
Tungsten was selected in this example because it simulates a very common method of producing x-rays, the x-ray tube.

16. Bremsstrahlung
When an electron enters a target material, it produces Bremsstrahlung x-rays which emanate in ALL directions.

17. X-Ray Unit
For example, in an x-ray tube, a cloud of free electrons is produced by heating a filament with an electric charge. The filament is similar to that which is found in any commercially available incandescent light bulb. The free electrons would hover around the filament were it not for a potential difference which is established with some electrical source. The portion of the tube where the filament is located is negatively charged and the target is positively charged. The free electrons are thus attracted to the target. They are accelerated across an open space (preferably a vacuum to preclude loss of energy by interaction with air molecules) and then ultimately strike the target.
Although the tungsten target appears to us to be a solid piece of metal, from the viewpoint of the electrons, the tungsten target is in reality a collection of tungsten atoms. Each atom, consisting of positively charged protons and negatively charged electrons orbiting around the nucleus, has the capability of attracting or repelling the accelerated electrons so that they lose the energy imparted to them by the potential difference as they travel in a confused path through the target.
In reality an x-ray tube is very inefficient for producing x-rays. Most of the energy of the electrons is dissipated as heat during low energy interactions in the target. However, a few percent of the electrons transfer their energy by emitting x-ray photons. The x-rays are of course emitted isotropically (in all directions) as noted previously, however, in a typical medical or industrial x-ray unit, it is desirable to focus the x-rays in a specific direction so they can be applied to the part being studied. For this purpose, shielding usually surrounds the target to stop all of the radiation except for the small “window” through which the useful x-rays are permitted to exit the unit.

18. Diagnostic Medical X-Ray Unit
Since so much of the energy is transferred to the target as heat, the target literally glows and, given enough heat, would eventually melt. To minimize the possibility of this occurring in diagnostic medical x-ray units, the target is spread out over the rim of a disk such that the electrons only strike a very small portion of the disk. The remainder of the disk aids in dissipating the heat. However, this would not be much of an improvement over the target in the previous slide were it not for the fact that the disk is rotated very rapidly. Using this technique, even though the electrons are focused to a very small spot, as the disk rotates, the spot continuously changes location so the heat is dissipated much more efficiently.

19. Characteristic Radiation
incident
electron
vacancy
created
electron
transition
x-ray
emitted
In a second process radiation is emitted by the electrons of the anode atoms when incoming electrons from the cathode knock electrons near the nuclei out of orbit and they are replaced by other electrons from outer orbits
The production of characteristic radiation is very different from the production of Bremsstrahlung. As we discussed earlier, when an electron orbiting around a nucleus is either excited or ionized, a vacancy is created where the electron formerly existed. When an electron from a higher orbit “falls” down to fill the vacancy, it becomes more tightly bound and thus must lose energy. The amount of energy it loses depends on the difference in the energy levels of the two orbits. If the difference in the energy levels were 20 keV, then an x-ray with an energy of 20 keV would be created.
Since the x-rays produced by this process can only have discrete energies equal to the amount of energy separating two orbits, the x-rays produced are called characteristic x-rays because the energy of these x-rays is “characteristic” of the two orbits between which the transition took place.
It is clear that the energy can vary depending on whether the transition occurs between an L-shell and a K-shell, or an M-shell and a K-shell, or an M-shell and an L-shell. The transitions can be between adjacent shells (such as M to L) or it can be between widely separated shells (such as N to K, bypassing M and L). Thus there are very many different characteristic x-rays that can be produced in any given atom.

20. Characteristic Radiationw M N L K
This graphic demonstrates how transitions can occur between electron orbits around a nucleus. It also provides an example of the various characteristic energies possible from those transitions. Above the O-shell there exists optical orbits between which transitions can occur. The energy difference between these orbits is so small that the energy emitted is in the optical range rather than the x-ray range. Such optical emissions are useful for applications such as Thermoluminescent Dosimeters.

21. Polyenergetic vs Monoenergetic X-Rays Polyenergetic Energy E1 E6 E7 E8
Emax
As the electrons traverse a target, the amount of energy lost during each interaction with an atom can vary from a very small amount of energy which could result in a low energy x-ray to a large amount of energy resulting in a high energy x-ray. The maximum energy that the electron can lose is equal to the total amount it possesses which depends on the potential difference which accelerated it. If, for example the electron was accelerated by a voltage of 100 kVp (100,000 volts potential), then the maximum energy that the electron can lose as it traverses the target is 100 keV (the maximum that it possessed).
So if we were to look at a plot of the energy of the x-rays produced as a result of Bremsstrahlung interactions, we would see a lot of low energy x-rays with the number decreasing until we reached the maximum energy possessed by the electrons. The probability of an electron losing all of its energy in one cataclysmic interaction producing an x-ray with an energy equal to Emax is small. As a result of this variation, Bremsstrahlung radiation can be considered Polyenergetic since there is more than one possible energy transferred to the target.

22. Polyenergetic vs Monoenergetic X-Rays missing due to filtration
Energy
Polyenergetic E1 E6 E7 E8 E9
E10
E11
E12
E13
E14 E2 E3 E4 E5
Polyenergetic vs
Monoenergetic X-Rays
missing
due to
filtration
If you have seen drawings of the output of x-ray units you may be confused since the drawings typically look like the green curve in the above graphic. However, the representation of Bremsstrahlung production on the previous slide and this one are consistent. The blue area in this graph is usually eliminated from the actual polyenergetic spectrum as a result of either inherent or added filtration in the actual system. For medical x-ray units, the low energy x-rays are not capable of penetrating the body part being evaluated but can produce radiation exposure so it is best to eliminate them resulting in the green curve more typically seen.

23. Polyenergetic vs Monoenergetic X-Rays Monoenergetic Polyenergetic
Energy
Polyenergetic E1 E6 E7 E8 E9
E10
E11
E12
E13
E14 E2 E3 E4 E5
Monoenergetic
Eeff
Polyenergetic vs
Monoenergetic X-Rays
Characteristic radiation is monoenergetic. It consists of x-rays of a single energy representing the energy lost by the electron as it transfers from a higher orbit to a lower orbit. Of course there may be many characteristic x-rays produced, but each one is monoenergetic.
In reality, the Bremmstrahlung x-ray spectrum although termed polyenergetic is actually itself a collection of monoenergetic x-rays. However, the spectrum of individual energies are all produced together so that it appears as a polyenergetic spectrum.
For convenience, the polyenergetic beam can be “simulated” by a monoenergetic beam with an effective energy = Eeff . For example, if a beam of electrons are accelerated by a potential of 100 kVp, the resulting x-ray spectrum can be termed 100 kVp x-rays or they can be referred to as a polyenergetic beam of x-rays with an effective energy of say 32 keV (the actual effective energy would have to be determined). The 100 kVp statement tells us how the x-rays were produced but the effective energy statement tells us how they behave.
The effective energy will be used later in the discussion of filtration, half value later and attenuation coefficients.

24. Characteristic Radiation
When characteristic x-rays are produced along with Bremsstrahlung x-rays, the spectrum appears to be a combination of the two.
In the two cases shown in this slide, both Bremsstrahlung spectra terminate on the right at the energy equal to the maximum potential with which they were produced. For the Molybdenum target produced at 28 kVp, the spectrum terminates at 28 keV and for the Tungsten target produced at 100 kVp, the spectrum terminates at 100 keV.
It should be noted that they also both terminate on the low energy side at about 8 keV. Remember that Bremsstrahlung x-rays are being produced below this point but that the spectra displayed are the result of measurements on actual x-ray units so that the inherent and added filtration eliminate these low energy x-rays.
One additional point to clarify is the abrupt drop in the molybdenum Bremsstrahlung spectrum above 20 keV. One would have assumed that the spectrum would drop off gradually as indicated by the dotted line. The abrupt drop is due to the K-edge effect. The binding energy of the K-shell in Molybdenum is 20 keV. Incident electrons with this amount of energy are able to eject these tightly bound electrons if the incoming electron transfers all its energy to the bound electron. If this occurs, that incoming electron has no additional energy to produce x-rays via Bremsstrahlung so there is a significant reduction in the Bremsstrahlung x-ray production at this point. As the energy of the incoming electrons increases, some can still eject the bound K-shell electrons but others can also produce Bremsstrahlung x-rays above 20 keV (given the total number of incident electrons above 20 kVp, the existence of the K-edge results in a much smaller probability of producing the Bremsstrahlung x-rays that would normally be expected).
Although it is not specified here, most Molybednenum x-ray units also incorporate a Molybdeum filter so that the higher energy x-rays can undergo the photoelectric effect in the filter but that will be covered in a future lecture.
Remember also that the probability of single Bremsstrahlung interaction (that is, an interaction where all of the incoming electron’s energy is converted to a high energy x-ray) decreases as energy increases so we would normally expect to see few of these high energy x-ray produced. When combined with the increased probability of ejecting K-shell electrons, the number of higher energy x-rays is significantly reduced.
A similar reduction is seen in the Tungsten spectrum just above 67.2 keV but not as dramatic since Tungsten x-ray units typically use Aluminum filters. A similar dramatic reduction to that seen in the Molybdenum plot would likely be seen if a Tungsten filter were used along with the Tungsten target.
Superimposed on the Molybdenum spectrum are the 17.5 keV and 19.6 keV K-shell monoenergetic characteristic x-ray peaks (L  K and M  K) and superimposed on the Tungsten spectrum are the 59.3 keV and 67.2 keV K-shell monoenergetic characteristic x-ray peaks (L  K and M  K).

25. Characteristic Radiationw M N L K
On the previous graphic we noted that the characteristic peaks for Tungsten were 59.3 keV and 67.2 keV. Here we can see where they originate. The L  K transition yields 70,000 – 11,000 = 59,000 eV or 59 keV while the M  K transition yields 70,000 – 2,500 = 67,500 eV or 67.5 keV.

26. Auger Electrons
Auger electrons are a special case of Internal Conversion.
During the Internal Conversion Process, a gamma photon from the nucleus interacts with and transfers all of its energy to a tightly bound (K-shell) orbital electron.
The electron is ejected from the atom with considerable energy, equal to that of the initial gamma photon minus the binding energy.
Note that for Internal Conversion, the K-shell electron is ejected by a GAMMA ray originating from WITHIN the nucleus of the atom itself.
This differs from the situation we have previously discussed where the K-shell electron was ejected by an incident ELECTRON originating outside the atom or the case which will be discussed in a future lecture where the K-shell electron is ejected by a PHOTON (gamma or x-ray) originating outside the atom.

27. Auger Electrons characteristic x-ray Auger electron
When a vacancy is created in an orbit, an electron from a higher orbit descends to the lower orbit to fill the vacancy. This will leave a vacancy in a higher orbit which is then filled by an electron from a still higher orbit. This cascade of electrons results in a cascade of characteristic x-rays representing the difference in the orbital energy levels over which the electrons traveled. Normally these characteristic x-rays escape the atom just as gamma photons normally escape the nucleus. However, occasionally, a characteristic x-ray may interact with a loosely bound electron in an outer orbit, transferring all of its energy to the electron and ejecting it from the atom. This Auger electron possesses all of the energy of the characteristic x-ray minus the small binding energy.
So it can be seen that the Auger electron results from an “internal conversion” type process because the x-ray that ejects the electron originated from within the atom rather than originating from some outside source.

28. Where to Get More Information
Cember, H., Johnson, T. E, Introduction to Health Physics, 4th Edition, McGraw-Hill, New York (2009)
International Atomic Energy Agency, Postgraduate Educational Course in Radiation Protection and the Safety of Radiation Sources (PGEC), Training Course Series 18, IAEA, Vienna (2002)