1. Ch6 X-ray Producing X-ray Moseley formula X-ray diffraction
Compton effect
Absorption of x-rays

2. Some Words X-ray Molybdenum (钼) Moseley’s model Compton scattering
Moseley's empirical formula
electromagnetic spectrum
Bremsstrahlung (轫致辐射)
Characteristic x-ray
Bombard (轰击)
Graphite (石墨)
Vacancy
Molybdenum (钼)
Compton scattering
Interaction
Absorption coefficient
Absorption edge
Positron (正电子)
Photoionization
Pair formation
Attenuate (衰减)
Binding energy
Binding energy: (1) The net energy required to decompose a molecule, an atom, or a nucleus into its components. (2) The net energy required to remove an atomic electron to an infinitely remote position from its orbit.

3. X-rays
X-rays mean electromagnetic radiation which has a wavelength shorter than that of ultraviolet light nm, 1-500keV, or 1-100keV
X-rays can be produced when electrons, accelerated through a large potential difference, collide with a metal target.
A plot of x-ray intensity per unit wavelength versus the wavelength consists of sharp peaks or lines superimposed on a broad continuous spectrum (Bremsstrahlung).
The cut-off frequency of the Bremsstrahlung is determined by the KE of the impinging electrons.
X rays originate from the interaction between the electrons and the metal target. X-ray production is the inverse of the photoelectric effect.
For x-rays, the shorter wavelength end overlaps gamma rays and the longer-wavelength end overlaps ultraviolet.
Bremsstrahlung means braking radiation in German. It takes place when the electrons decelerate or brake upon hitting the target.

4. X-ray spectrum
X-ray is produced when a molybdenum target is bombarded with electrons of 35keV.
It includes Bremsstrahlung continuium & characteristic lines.
There is cut-off frequency.
When the electron gives all its energy to radiate, the photon gets the maximum energy, the smallest wavelength.

5. Brehmsstrahlung
"Bremsstrahlung" meaning "braking radiation" describes the radiation which is emitted when electrons are decelerated or "braked" when they are fired at a metal target.
Accelerated charges give off electromagnetic radiation, and when the energy of the bombarding electrons is high enough, that radiation is in the x-ray region of the electromagnetic spectrum.
It is characterized by a continuous distribution of radiation which becomes more intense and shifts toward lower wavelength when the energy of the bombarding electrons is increased.

6. Characteristic x rays
There must be a vacancy in a subshell of an atom to produce characteristic x-rays.
The bombarding electrons can eject electrons from the inner shells of the atoms of the metal target.
Those vacancies will be quickly filled by electrons dropping down from higher levels, emitting x-rays with sharply defined frequencies associated with the difference between the atomic energy levels of the target atoms, called characteristic x-rays.
Line spectra: The exciting electron must remove an atomic electron from an inner shell. The resulting hole id filled by outer electrons, and their binding energy is released in the form of characteristic light quanta.

7. K, L, M series in x-ray K lines involve K shell of a metal atom.
K shell electron is knocked out of the atom.
An electron in a outer shell falls into the K shell.
L lines involve L shell of a metal atom.
L shell electron is knocked out of the atom.
An electron in a outer shell falls into the L shell.

8. Moseley plot
When the square root of the frequencies of the characteristic x-rays from the elements is plotted against the atomic number, a straight line is obtained.
Moseley measured the frequencies of the characteristic x-rays from a large fraction of the elements of the periodic table and produces a plot of them which is now called a "Moseley plot".

9. Moseley’s formula
Moseley showed that the characteristic x-rays followed a straight line when the atomic number Z versus the square root of frequency was plotted.
With the insights gained from the Bohr model, we can write his empirical (经验的) relationship as follows:
hRc=13.6eV

10. X-ray diffraction
Like electron diffraction, x-rays can be diffracted by a crystal.
When x-rays are incident on a crystal in which atoms are arranged in regular array and act as an optical grating, the scattered waves will interfere in some directions.
The atoms in a crystal may be thought of as families of parallel planes known as Bragg planes.
The Bragg equation for maxima in the diffraction pattern is:

11. Compton effect
Compton effect, Compton ( ) showed that monochromatic X rays are scattered by graphite (石墨), and their wavelength increases by:
The collision between a photon and an electron is regarded as an elastic collision.
Compton wavelength of electron:

12. Compton scattering
Compton first to measure photon-electron scattering in 1922.
When the incoming photon gives part of its energy to the electron, then the scattered photon has lower energy.
The wavelength change in such scattering depends only upon the angle of scattering for a given target particle.
The scattering of photons from charged particles is called Compton scattering after Arthur Compton who was the first to measure photon-electron scattering in 1922.

13. Photon interaction with matter
There are three ways:
Photoionization, giving all of the energy to an electron.
Compton scattering: giving part of the energy to the electron and the remainder to a lower energy photon.
Pair production: At sufficiently high energies (>1.02MeV), the photon can create an electron positron pair.
Generally, x-ray’s interaction is mainly in first two ways.

14. X-ray absorption
X-rays, like other electromagnetic radiation, are absorbed and scattered on passing through matter.
The transmitted intensity is given by:
I0: incident intensity,
μ: absorption (Photoionization absorption + scattering) or attenuation coefficient, mass absorption coefficient,
x: the thickness of the material irradiated,
µ depends strongly on x-ray energy E and atomic number Z, and on the density ρand atomic mass A.
The extinction is the sum of scattering and absorption. In order for an atom to absorb x-ray, an electron must excited from an inner shell into a less strongly bound state. Absorption is usually associated with ionization.

15. Absorption edge
If the wavelength of the X-rays is reduced so that their energy is equal to one of the energies of the atomic levels of the absorber, a sudden increase in absorption is observed.
It corresponds to the photon energy to knock out an inner electron.
In X-ray spectrum, the K-absorption edge for each element is slightly less than that for the K-emission spectrum.
This feature of x-ray absorption edge has some applications, such as filter, spectrum differentiation & coronary angioplasty.
Absorption
Photon Energy
PTCA: Percutanerous Transluminal Coronary Angioplasty
In addition, µ has sharp Absorption Edges corresponding to the characteristic core-level energies of the atom.

16. Example1
Question: The K absorption edge wavelength for uranium (Z=92) is 0.107Å and its Kα line is 0.126Å. Find the wavelength of its L absorption edge.
Answer:
n=inf
The binding energy of an electron in a shell equals the negative of the energy of that shell. L Kα K

17. Example 2
Question: A beam of electrons with 100keV are bombarding the target. The binding energies for the inner shells for the target atom are listed in the table. Find the possible x-rays and their wavelength.
Solution: Determine the energy level of subshells from the binding energy. Using selection rule to determine the possible transitions and then calculate the wavelengths.
Total: 12 lines: K-alpha (2), K-beta (2), L-alpha (7)
shell K LI
LII
LIII MI
MII
MIII
MIV MV
electron 1s 2s 2p 3s 3p 3d
BE (keV)
20.00
2.866
2.625
2.520
0.505
0.410
0.393
0.230
0.227
For Mo (Z=42), 1s2, 2s22p6, 3s23p6, 3d104s24p6, 4d55s

18. The transitions M shell L shell Ⅰ Lα K shell Kα Kβ 2D5/2 2D3/2 2P3/2V 3d
M shell IV 3d Ⅲ 3p Ⅱ 3p Ⅰ 3s 1 2 1 2 3 4 5 6 7 8
L shell Ⅲ
2P3/2
2P1/2
2S1/2 2p Ⅱ 2p Ⅰ 2s Lα 1 2
K shell 1s
2S1/2 Kα Kβ