X – Rays A-LEVEL PHYSICS

X – Rays A-LEVEL PHYSICS

X – Rays

X- rays are short wavelength electromagnetic waves which are produced when cathode rays are stopped by heavy metals.

Production of X – rays

Mode of operation

A low voltage is applied across the filament and heats the filament. Electrons are emitted by the filament by thermionic emission. The concave focusing cathode focuses the electrons from the filament onto the target.

A very high alternating voltage is applied between the filament and the anode. During the half cycles when the anode is at a positive potential relative to the cathode, electrons are accelerated across the tube. No electrons flow to the anode when the anode is at a negative potential relative to the cathode.

When the cathode rays (electrons) strike the target, 99% of the kinetic energy of electrons is dissipated into heat  while 1% is turned into X-rays.

The heat generated at the target is cooled by means of the copper cooling fins mounted on the copper anode. Heat is conducted  from the target away from the tube by conduction and radiation.

The electron current, I in an X-ray tube in operation is given by I = ne, where n is the number of electrons per second and e is the electronic charge.

Intensity of X-rays (Quantity)

The intensity of X- rays in an X – ray tube is proportional to the number of electrons colliding with the target. The number of electrons produced at the cathode depend on the filament curret. The greater the heating current, the greater the number of electrons produced and hence more x- rays are produced. Therefore the intensity of X- rays is controlled by the filament current.

Penetration of X – rays ( quality)

Penetration power of X-rays depends on the kinetic energy of the electrons striking the target. The higher the accelerating voltage, the faster the electrons produced. Faster electrons posses higher kinetic energy and shorter wavelength x-rays of greater penetration power are produced. Hence penetrating power of X-rays is determined by the accelerating Voltage across the tube.

Hard and soft X- rays

Hard x-rays have a high penetrating power. This because they have very short wavelengths. They are produced when a high p.d is applied across the tube.

Soft X-rays are produced by electrons moving at relatively lower velocities than those produced by hard x –rays. They have less energy, longer wavelengths, hence less penetration power compared to hard x-rays.

Hard x-rays can penetrate flesh but are absorbed by bones. Soft x-rays are used to show malignant growths since they only penetrate soft flesh. They are absorbed by such growths.

Properties of X –rays

They travel in a straight line at a speed of light

They are not deflected by both magnetic and electric fields. This indicates that they carry no charge.

They penetrate all matter to some extent. Penetration is least in materials with high density and atomic number e.g. lead.

They ionise gases through which they pass.

They affect photographic plates just like light does.

They cause fluorescence in some materials.

They cause photoelectric effect when they are illuminated on certain metal surfaces.

They are diffracted by crystals leading to an interference pattern.

Examples

In an x-ray tube 99% of the electrical power supplied to the tube is dissipated as heat. If the accelerating voltage is 75kV and power of 742.5W is dissipated as heat, find the number of electrons arriving at the target per second.

EMBED Equation.3

Hence Power supplied =  EMBED Equation.3

But power = VI

Hence 75000I = 750

I = 0.01A

But I = ne

= 1.6×10-19n

Therefore n = 6.25×10¹⁶ per second

After long exposure to x-rays, the photographic plate is developed and printed. A regular pattern of dark spots called Laue spots are observed around the central dark image. The pattern is due to scattering of x-rays by interaction with electrons in the atom of the crystal. The regularity of the spots implies that atoms in the crystal are arranged in a regular pattern.

Consider a beam of monochromatic x-rays incident on a crystal such as KCl at a glancing angle θ.

Let d be the interatomic or interplanar spacing and λ the wave length of the x-rays. A small fraction of the incident x-rays is scattered by each atom. The scattered x-rays interfere constructively in those directions for which the angle of incidence is equal to the angle of reflection.

Example

X-rays of wavelength 10^-10m are diffracted from a set of planes of rubidium Chloride. The first diffraction maxima occurs at 8.8°. calculate the interplanar spacing.

Let M be the molecular mass of NaCl, ρ density and N_a Avogadro’s number.

Mass per molecule = EMBED Equation.3

Volume associated with one molecule = EMBED Equation.3

One molecule of NaCl has two atoms, hence volume associated with one atom =  EMBED Equation.3

But volume associated with one atom = d3.

Hence  EMBED Equation.3

X-ray spectra in an x-ray tube

There are two spectra;  continuous and line/prominent/ characteristic spectra.

The intensity of x-rays plotted as a function of wavelength has the features shown below. The line  spectrum is superimposed on the continuous spectrum.

Continuous spectrum

This arises from multiple collisions of electrons with target atoms. Different amounts of energy are lost during these collisions. The x-rays given off when the electrons are decelerated will have wavelengths varying from a certain minimum value λ_min to infinity.

When an electron loses all its energy in a single collision with an atom of the target, a most energetic x-ray photon is given off. The kinetic energy of the electrons equal to eV, where V is the accelerating voltage between a filament and the anode. It  is converted into electromagnetic.

Equation (1) is called the Hunt- Duane equation . λmin represents the minimum wavelength of the X-ray produced for a given accelerating voltage V. It is also called-cut off wavelength.

Uses of X-rays

1.  Structural analysis, stresses, fractures in solids, castings and welded joints can be analysed by examining X-ray photograph.

2.  Crystallography; Orientation and identification of minerals by analysis of diffraction patterns using Bragg’s law.

3.   Medical uses;

(i) Analytical uses. These include location of fractures, cancer and tumour/defective tissue absorbs x-rays differently from normal tissue.

(ii) Therapeutics use for destroying cancerous cells and tumours. detection of fire arms at international airports.

THIS VIDEO EXPLAINS MORE ABOUT X-RAYS