# X-Rays & its Production

X-rays are extremely short wavelength electromagnetic radiation, first produced by W.C. Roentgen in 1895 by bombarding a heavy metal anode with high energy electrons.

X-ray emission is the inverse of the photoelectric effect : in the photoelectric effect, the energy of a photon is transformed into the kinetic energy of a photoelectron, while during X-ray emission, the kinetic energy of a photon is converted into X-rays.

The experimental arrangement for producing X-rays is shown in the figure. The filament is heated to high temperatures, and then, it starts emitting electrons due to thermionic emission. These electrons are then accelerated by a very high potential difference (between the filament and the target) and the electon beam is focussed onto a metal anode (made of a heavy metal like Cu, W etc.)

The following processes occur :

(i)   An electron loses a part of its kinetic energy and continues to move with the remaining energy until it hits another atom of the target. Part or whole of the energy lost by the electron is converted into a photon. This process is known as bremsstrahlung (breaking radiation)- as it leads to the electron getting decelerated by the target. It is impossible to explain using classical ideas, the continuous spectrum of X-rays generated during this process – especially the existence of a minimum wavelength (or maximum frequency). This minimum wavelength does not depend on the target material.

(ii) The other process produces peaks within the X-ray spectrum that depend on the target material. The high energy electrons “knock off” the innermost electrons of the atoms of the target material causing a vacancy. This vacancy is filled by an electron that ‘jumps‘ from one of the outer shells.   The energy of the photon emitted is characteristic of the target atom.

If the potential difference between the filament and the target is V then the kinetic energy of the electron just before it hits the target is

K.E. = eV

Energy of the X-ray photon, ΔE = hc/λ

ΔE is the fraction of K.E. of electron that gets converted into photon. l is the wavelength of the photon.

Wavelength of the X-ray’s photon

λ = hc/ΔE    as ΔE ≤ eV

⇒   λ ≥ hc/eV ⇒ λmin = hc/eV

λmin is known as cut off wavelength.

The adjoining graph shows the variation of the intensity of X-rays coming out of the tube with wavelengths.   At some sharply defined wavelengths (Ka,, Kb) the intensity of the emitted radiation is very large. These x-rays are known as characteristic X-rays.

The wavelengths of continuous X-rays depends only on the potential difference between the filament and the target.

#### Production of characteristic X-rays:

Suppose that a fast moving electron knocks out an inner electron from an atom of the target element. A vacancy is created, an electron from filled higher energy level jumps into the vacancy and the excess energy is released as a photon. This process produces characteristic X-rays.

If the vacancy is created in K shell and electron from the L shell fills the vacancy then the emitted photon is a Kα – X-ray. If a vacancy is created in the K-shell and an electron from the M shell fills this vacancy then the X-ray emitted is known as a kβ X-ray.

### Production of characteristic X-rays

Suppose that a fast moving electron knocks out an inner electron from an atom of the target element. A vacancy is created, an electron from filled higher energy level jumps into the vacancy and the excess energy is released as a photon. This process produces characteristic X-rays.

If the vacancy is created in K shell and electron from the L shell fills the vacancy then the emitted photon is a Kα – X-ray. If a vacancy is created in the K-shell and an electron from the M shell fills this vacancy then the X-ray emitted is known as a Kβ X-ray.

$\large \lambda_{K_\alpha} = \frac{h c}{E_L – E_K}$

$\large \lambda_{K_\beta} = \frac{h c}{E_M – E_K}$

;   where Ek , EL, EM are the electronic energy levels

###### Moseley’s law :

Moseley studied the nature of characteristic X-rays experimentally. His observations led to the empirical result :

√ν = a(Z−b)

where ν = frequency of the X-ray and a and b are constants, characteristic of the emitter.

⇒   ν = a2 (Z−b)2                     … (i)

From Bohr’s atomic theory,

$\large \nu = \frac{E_1 Z^2}{h} (\frac{1}{n^2} -\frac{1}{m^2} )$ …(ii)

Comparing these two expressions, we can conclude that for an atom having a high atomic number, Z can be replaced by (Z-b).

For Ka – X-ray       b = 1

$\large \lambda_{K_\alpha} = \frac{h c}E_1(Z-1)^2{1 – \frac{1}{4}}$

$\large = \frac{4}{(\frac{E_1}{hc}) 3(Z-1)^2}$

where E1 = 13.6 eV

$\large \lambda_{K_\alpha} = \frac{4}{3R(Z-1)^2}$

Here R ≡ Rydberg constant

#### Soft and hard X-rays

Short wavelength X-rays are called hard X-rays and long wavelength X-rays are known as soft X-rays.