We know that, x-rays are produced when high velocity electrons hit the target. If we plot a graph between x-rays intensity I(λ) and wavelength λ, it will have the general shape as shown in figure (below). In figure we see a curve, such a curve a called a x-rays spectrum. So it is clear that from this above figure that, there exist a wavelength λmin below which there is no radiation. So that’s why λmin is called cut off wavelength. 

The x-rays spectrum consist of two distinct parts-  

1. Continuous spectrum

The continuous part ABCDE of the curve is called continuous or which spectrum. It consists of radiations of all wavelengths between λmin to ∞. The continuous spectrum arises because of the rapid de-acceleration of the electrons by the target material.

2. Characteristic spectrum- 

The shape peaks observed in the curve at particular wavelength are known as characteristic x-rays. These arises when an orbital electrons jumps between the orbit of the atom in the target. The position of the peak depends on the nature of the target material. 

Mechanism for production of x-rays---

Continuous spectrum-

When a fast moving electrons strikes a target, it experience an attractive force due to nucleus of the target atom, due to which the path of the electron change. 

The deviation of the path of electron is equivalent to its collision with nucleus, because of this collision, electron losses some of its kinetic energy which appears as x-rays photon. 

If E is the initial kinetic energy of the electron and E’ is the final kinetic energy, then (E-E’) is the energy carried by the photon of x-rays. If Ѵ is the frequency of the photon, then energy of x-rays photon is - h Ѵ=E-E’ -----(1).

Thus electron may suffer several collisions with various nuclei before coming to rest and each collision is accompanied by the emission of x-rays photon. Since there are a number of electrons which suffer from collision and they gives rise to x-rays photons of almost all wavelength. These photons produced by many electrons make whole make up the continuous spectrum.

Expression for λmin 

According to classical theory, spectrum should contain all wavelength from 0 to ∞. But according to quantum theory energy is emitted in the form of photons. The wavelength of the wave measures the energy of each photon. 

Suppose an electron loss all its kinetic energy ion one collision, the E’=0 and the photon is emitted with maximum energy. So equations (1) becomes-
                       E=hѴmax.-----(2)
The maximum frequency corresponds to minimum wavelength, 
                       E=hc/λmin-----(3)
Suppose this electrons has been accelerated then a potential difference before striking target, then,
                        E=eV------(4)
Now from (3) and (4), we get, 
                                 eV=hc/λmin
                                 λmin=hc/eV------(5).

Since h,c and e are constant., λmin depends upon on V. Also λmin does not depend upon the target material, hence it is same for all materials. The cut off wavelength (λmin) represents the complete conversion of electrons kinetic energy to an x-ray photon. 

Characteristic spectrum-

When the bombarding electrons in the x-rays strikes the target, they have sufficient energy to eject the orbital electrons of the target atom.


Suppose an incident electron knock’s out an orbital electron from the k-shell. This electrons leaves the atom with a vacancy in k-shell, which is shown in below figure (b).



The atom is now in excited state, the electron from any higher L,M,…..shell can fall into the vacant site in the k-shell accompanied by emission in the form of radiations as shown in figure(c). 


if an electron from L shell fall into K-shell , then amount of energy radiated will be
      hѴ1=E(L)-E(K)------(6)

Where E(L) and E(K) are the energies of Land K shells respectively. The transition of the electron from L-shell to K-shell creates a new vacancy in the K-shell which is filled by another electron from higher M-shell emitting radiation, then amount of radiations is given by-
                    hѴ2=E(M)-E(K)------(7)

Where E(M) is the energy of M-shell. This process continuous and we get a series of spectral lines corresponding to various electrons jumping.
The amount of energy radiated in each transition determine by the difference in energies of involved shells which depends on the atomic number of the target atom. Thus the radiations emitted are characteristic of the target atom. Every element has its own characteristic x-rays.