X - Rays

Objectives

• Introduction and production of X-Rays• Properties of X-Rays• Diffraction of X-Rays• The Bragg’s X-Ray spectrometer• Continuous spectra• Characteristics Radiation• Moseley’s law • Absorption of X-Ray• Compton effect • Applications of X-Rays

Introduction of X-Rays • Rontgen discovered X-rays in 1985 during some

experiments with a discharge tube. • He noticed that a screen coated with barium

platinocyanide present at a distance from the discharge tube. Rontgen called these invisible radiations “X-rays”.

Finally, he concluded that X-rays are produced due to the bombardment of cathode rays on the walls of the discharge tube.

• X-rays are highly penetrating and it can pass through many solids.

• X-rays occur beyond the UV region in the electromagnetic spectrum.

• Their wavelengths range from 0.01 to 10 Å.

Production or Generation of X-raysX-rays are produced by an X-ray tube. The

schematic of the modern type of X-ray tube is shown in above figure.

It is an evacuated glass bulb enclosing two electrodes, a cathode and an anode.

The cathode consists of a tungsten filament which emits electrons when it heated. The electrons are focused into a narrow beam with the help of a metal cup S.

The anode consists of a target material, made of tungsten or molybdenum, which is embedded in a copper bar.

Water circulating through a jacket surrounding the anode and cools the anode. Further large cooling fins conduct the heat away to the atmosphere.

• The face of the target is kept at an angle relative to the oncoming electron beam. A very high potential difference of the order of 50 kV is applied across the electrodes.

The electrons emitted by the cathode are accelerated by the anode and acquire high energies of order of 105 eV. When the target suddenly stops these electrons, X-rays are emitted.

• The magnetic field associated with the electron beam undergoes a change when the electrons are stopped and electromagnetic waves in the form of X-rays are generated.

• The grater of the speed of the electron beam, the shorter will be the wavelength of the radiated X-rays. Only about 0.2 % of the electron beam energy is converted in to X-rays and the rest of the energy transforms into heat. It is for the reason that the anode is intensively cooled during the operation of X-ray tube.

• The intensity of the electron beam depends on the number of electron leaving the cathode. The hardness of the X-rays emitted depends on the energy of the electron beam striking the target. It can be adjusted by varying the potential difference applied between the cathode and anode. Therefore, the larger potential difference, the more penetrating or harder X-rays.

Properties of X-Rays…They have relatively high penetrating power.

They are classified into Hard X-rays & Soft X-rays.

The X-rays which have high energy and short wavelength is known as Hard X-rays.

The X-rays which have low energy and longer wavelength is known as Soft X-rays.

X-rays causes the phenomenon of flouroscence.

On passing through a gas X-rays ionize the gas.

Properties of X-Rays…

They are absorbed by the materials through which they traverse.

X-rays travel in straight line. Their speed in vacuum is equal to speed of light .

X-rays can affect a photographic film.X-rays are undeflected by electric field or

magnetic field.

Diffraction of X-Rays – Bragg’s law

Consider a crystal as made out of parallel planes of ions, spaced a distance d apart. The conditions for a sharp peak in the intensity of the scattered radiation are: 1. That the X-rays should be secularly reflected by the ions in any one plane. 2. That the reflected rays from successive planes should interfere constructively.

• Path difference between two rays reflected from adjoining planes: 2dsinθ,

• For the rays to interfere constructively, this path difference must be an integral number of wavelength λ,

nλ =2dsinθ ------- (1)

Bragg angle is just the half of the total angle by which the incident beam is deflected.

The Bragg’s X-Ray spectrometer• An X-ray diffraction experiment requires,

• X-ray source• The sample• The detector

• Depending on method there can be variations in these requirements. The X-ray radiation may either monochromatic or may have variable wave length.

• Structures of polycrystalline sample and single crystals can be studied. The detectors used in these experiments are photographic film.

The schematic diagram of Bragg’s X-ray spectrometer is given in above.

• X-ray from an X-ray tube is collimated by passing team through slits S1 and S2. This beam is then allowed to fall on a single crystal mounted on a table which can be rotated about an axis perpendicular to the plane of incident of X-rays. The crystal behaves as a reflected grating and reflects X-rays. By rotating the table, the glancing angle θ at which the X-ray is incident on the crystal can be changed. The angle for which the intensity of the reflected beam is maximum gives the value of θ. The experiment is repeated for each plane of the crystal. For first order reflection n = 1 so that, λ = 2d sinθ; for n = 2, 2λ = 2d sinθ; ……., and so on.

• A photographic plate or an ionization chamber is used to detect the rays reflected by the crystal.

Continuous or Bremsstrahlung X-rays• "Bremsstrahlung" means "braking radiation" and

is retained from the original German to describe 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.

Continuous X-rays…

Continuous X-rays…• It is characterized by a continuous distribution of

radiation which becomes more intense and shifts toward higher frequencies when the energy of the bombarding electrons is increased.

• The curves above are who bombarded tungsten

targets with electrons of four different energies.

• The continuous distribution of x-rays which forms the base for the two sharp peaks at left is called "Bremsstrahlung" radiation.

Characteristic X-rays• Characteristic X-rays are emitted from heavy

elements when their electrons make transitions between the lower atomic energy levels.

Characteristic X-rays…

• Characteristic X-rays emission which shown as two sharp peaks in the illustration at left occur when vacancies are produced in the n = 1 or K-shell of the atom and electrons drop down from above to fill the gap.

• The X-rays produced by transitions from the n = 2 to n = 1 levels are called Kα X-rays, and those for the n = 3->1 transition are called Kβ X-rays.

• Transitions to the n=2 or L-shell are designated as L - shall X-rays (n= 3->2 is Lα, n = 4->2 is Lβ, etc.

Uses of Characteristic X-rays..

• Characteristic X-rays are used for the investigation of crystal structure by X-ray diffraction.

• Crystal lattice dimensions may be determined with the use of Bragg's law in a Bragg spectrometer.

Moseley’s law and its importance.• The English physicist Henry Moseley (1887-1915)

found, by bombarding high speed electrons on a metallic anode, that the frequencies of the emitted X-ray spectra were characteristic of the material of the anode.

• The spectra were called characteristic X-rays. • He interpreted the results with the aid of the

Bohr theory, and found that the wavelengths λ of the X-rays were related to the electric charge Z of the nucleus. According to him, there was the following relation between the two values (Moseley’s law; 1912).

1/λ = c(Z - s)2

Where, c and s are constants applicable to all elementsZ is an integer.

When elements are arranged in line according to their position in the Periodic Table , the Z value of each element increases one by one.

Moseley correctly interpreted that the Z values corresponded to the charge possessed by the nuclei. Z is none other than the atomic number.

It was found that the characteristic X-ray of an unknown element was 0.14299 x 10-9 m. Thewavelength of the same series of the characteristic X-ray of a known element Ir (Z = 77) is 0.13485x 10-9 m. Assuming s = 7.4, estimate the atomic number of the unknown element.

Importance of Moseley’s law

• Atomic no. is more important than Atomic weight as it is equals to charge of nucleus.

• Difference between Ni, Co, Te & I etc., is explained when periodic table was constructed with atomic no.

• Moseley predicted the existence of elements with atomic no. 43, 61, 72 & 75. Thus, X-ray spectrum analysis new elements can be discovered.

Absorption of X-Ray When the X-rays hit a sample, the oscillating

electric field of the electromagnetic radiation interacts with the electrons bound in an atom.

A narrow parallel monochromatic x-ray beam of intensity I0 passing through a sample of thickness x will get a reduced intensity I according to the expression: ln (I0 /I) = μ x ------- (1)

Where μ is the linear absorption coefficient, which depends on the types of atoms and the density ρ of the material.

At certain energies where the absorption increases drastically and gives rise to an absorption edge. Each such edge occurs when the energy of the incident photons is just sufficient to cause excitation of a core electron of the absorbing atom to a continuum state, i.e. to produce a photoelectron.

The absorption edges are labeled in the order of increasing energy, K, LI, LII, LIII, MI,…., corresponding to the excitation of an electron from the 1s(2S½), 2s(2S½), 2p(2P½), 2p(2P3/2), 3s(2S½), … orbitals (states), respectively.

Thus, the energies of the absorbed radiation at these edges correspond to the binding energies of electrons in the K, L, M, etc.., shells of the absorbing elements.

Compton effect

A phenomenon called Compton scattering, first observed in 1924 by Compton, and provides additional direct confirmation of the quantum nature of electromagnetic radiation. When X-rays impinges on matter, some of the radiation is scattered, just as the visible light falling on a rough surface undergoes diffuse reflection.

• Observation shows that some of the scattered radiation has smaller frequency and longer wavelength than the incident radiation, and that the change in wavelength depends on the angle through which the radiation is scattered.

• Specifically, if the scattered radiation emerges at an angle φ with the respect to the incident direction, and if f and i are the wavelength of the incident and scattered radiation, respectively, it is found that,

Where, m0 is the electron mass.

• In figure, the electron is initially at rest with incident photon of wavelength and momentum p; scattered photon with longer wavelength f and momentum p and recoiling electron with momentum P. The direction of the scattered photon makes an angle φ with that of the incident photon, and the angle between p and p is also φ.

called Compton wavelength.

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• Compton scattering cannot be understood on the basis classical electromagnetic theory.

• On the basis of classical principles, the scattering mechanism is induced by motion of electrons in the material, caused by the incident radiation.

Applications of X-Rays…X-rays are used in industrial, medical, pure

science research and X-ray crystallography etc…

• X-rays are used to detect defects in radio valves.• X-rays are used to detect cracks in structures.• X-rays are used to analyses the structures of

alloys and other composite bodies by diffraction of X-rays.

• They are also used to study are structure of materials like rubber, cellulose, plastic, fibres etc…

• X-rays can destroy abnormal internal tissues.

Applications of X-Rays…• X-rays are used in analysis of crystal structure and

structure of complex organic molecule.• They are also used in determining the atomic

number and identification of various chemical elements.

• X-rays are used to detect fractures and formation of stones in human body.

• They are also being used for tumor treatment and for this purpose hard X-rays are used.

• X-rays are also used in X-ray crystallography for Laue method, Rotating crystal method, Powder method, etc….