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-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.
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.x-ray 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.
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. characteristic x-rays
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.
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. characteristic x- rays
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:
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:
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:
Compton scattering Compton first to measure photon-electron scattering in 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.
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.Compton scattering –Pair production: At sufficiently high energies (>1.02MeV), the photon can create an electron positron pair. electron positron pair Generally, x-ray’s interaction is mainly in first two ways.
X-ray absorption X-rays, like other electromagnetic radiation, are absorbed and scattered on passing through matter. The transmitted intensity is given by: –I 0 : 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 ρ and atomic mass A.
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
Example1 Question: The K absorption edge wavelength for uranium (Z=92) is 0.107Å and its K α line is 0.126Å. Find the wavelength of its L absorption edge. Answer: K L n=inf KαKα
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 KLILI L II L III MIMI M II M III M IV MVMV electron 1s2s2p 3s3p 3d BE (keV)
The transitions 3d 3p 3s p 2s LαLα KαKα KβKβ 1s Ⅰ Ⅱ Ⅲ Ⅰ Ⅱ Ⅲ IV V M shell L shell K shell 2 S 1/2 2 D 5/2 2 D 3/2 2 P 3/2 2 P 1/2 2 S 1/2 2 P 3/2 2 P 1/2 2 S 1/2