USA: +1-585-535-1023

UK: +44-208-133-5697

AUS: +61-280-07-5697


In the year 1895, Wilhelm Roentgen found that a highly penetrating radiation of unknown nature is produced, when fast moving electrons impinge on matter. Since the nature of these radiations was unknown at the point of invention, they were named as X-rays. They were soon found to travel in straight lines, remain unaffected by electric and magnetic fields, pass radially through opaque materials, and cause phosphorescent’ substance to glow. The faster original electrons, the more penetrating were the resulting X-rays; and greater the number of electrons, the greater was the intensity of X-ray beam.

X-rays are electromagnetic waves. Electromagnetic theory predicts that an accelerated electric charge will radiate electromagnetic waves and rapidly moving electron suddenly brought to rest is certainly accelerated. Radiation produced under these circumstances is given the German name bremsstrahlung (or breaking radiation).

Product of X Rays

X-rays are produced when fast moving hit a suitable target after being accelerated under high potential difference.

The schematic arrangement for production of X-rays is shown in Figure 10.11. It consists of an evacuated bulb in which there is a filament F and target T. A high potential difference of 50-100 kv is maintained between the filament, which acts as cathode and target acting anode. When the filament is heated by passing current, it emits electrons which are accelerated towards the target because of the potential difference. The target is shaped in such a way that its surface will be at an inclination of 450 to the impinging electron beam, so that X-rays are emitted in a direction perpendicular to that of the beam.

FIGURE 10.11 X-rays are produced by bombarding a metal target

When the accelerated electrons hit the target, they possess a kinetic energy, Ek = eV, where, e is the charge on the electron and V is the applied potential.

Properties of X-Rays

X-rays are having following properties:

  1. X-rays are electromagnetic waves of very short wavelength (= 1 A – 100 A).
  2. The speed of X-rays is vacuum is equal to velocity of light.
  3. They ionise the gas through, which they pass.
  4. 4.      They produce flourescence in several materials such as ZnS.
  5. They can affect the photographic plate.
  6. They remain undeflected by electric and magnetic fields.
  7. They also show the phenomena like interference and diffraction just like light rays.
  8. They are absorbed by the materials through which they traverse.
  9. X-rays undergo reflection and refraction according to laws of visible light

Continuous and Characteristic X-Rays

The X-ray emission consists of radiations of wavelength over a continuous range within a certain limit, but with varying intensity. A plot of the intensity of the various radiations so emitted as a function of wavelength is called the X-ray spectrum.
The X-ray spectrum of molybdenum is shown in Figure 10.12.

The spectrum is continuous with a sharp, well defined cut off on the lower wavelength side at λmin. No X-ray radiations with wavelength less than the cut off wavelength λmin are found to be present in the X-ray emission. The value of cut off wavelength λmin changes with a change in the applied voltage V  that accelerates the electron, but it does not depend on the material used for the target. But the intensity increases with increase in the atomic number of the element of which the target is made.

In addition to the continuous spectrum, there are several intensity peaks at certain wavelengths as shown in Figure 10.12. The radiation corresponding to these wavelengths are called the characteristic X-rays. The wavelength of the characteristic X-rays do not depend upon the applied voltage V, but depend on the material of the target.

During the collision with the target, most of the bombarding electrons lose their kinetic energy as heat. But, under certain circumstances, the kinetic energy of some of the electrons will be converted into electromagnetic radiations, which result in continuous and characteristic X-ray spectra, the explanation of which is given as follows:


Among the electrons that collide with the target, some succeed in penetrating into the interior part of the target atoms and interact with the nuclei present there. This interaction gives rise to the continuous spectrum, which is also known as bremsstrahlung (which in German meaning braking radiation).


 Let us consider one such electron with energy Ek approaching the nucleus. Since the
nucleus is positively charged, the electron, because its negative charge, experiences an attractive force towards the nucleus. As a result, it is deflected from its straight line path (Figure 10.13). Such deviation is equivalent to a radial acceleration towards the nucleus. As per classical electromagnetic theory, an accelerated charge must emit electromagnetic radiations continuously, and of all frequencies, which explains the continuous emission spectrum. However, the fact that, there is a lower wavelength cut off (i.e., λmin), in the spectrum cannot be explained from the classical view. But the same can be explained with the help of photon concept of Einstein, according to which the accelerated charge radiates energy in terms of quanta’s of energy hv. If hv1, hv2, hv3, …. are the energies of the different photons emitted by the electron as it is accelerated, and also if Ek is the energy with which the electron emerges out of the influence of nucleus, then we can write,

energy lost by the electron = Ek – E’k.

Total energy radiated in the form of photons.

= hv1 + hv2 + hv3 +……

By the conservation of energy rule

Ek – E’k = = hv1 + hv2 + hv3 +……

(assuming no energy is acquired by the nucleus).

Under the limiting conditions, one can say that, a photon with highest possible energy is produced under the condition that.

a.  The electron loses all its energy by the time, it emerges from the influence of nuclei, i.e.,

E’k = 0 and

b.  All the energy lost by the electron appears in the from of a single photon, emitted as an X-ray radiation.

Ek=h vmax

But Ek = eV

where, e is the charge on the electron, and V is the applied potential

where, c is the velocity of light, λmin is the shortest wavelength of X-rays radiated. Therefore, short wavelength limit is given by λmin. From here, we can conclude that with increase in potential across the tube, the value of λmin decreases. The relation represented by Equation (1) is known as Duane and Hunt law.

Substituting the values



The energetic electrons, which succeed in penetrating into the target are subjected to the Interaction with electrons and nuclei of the atoms in the target material. Those which interact with the nuclei give rise to continuous spectrum as explained earlier. The other electrons, in general, undergo multiple collisions with the atomic electrons and there by slowdown while losing their energy in the form of heat of the target. But occasionally, the collision may occur in such a way that, an incident electron transfers a large portion of its energy at once to an atomic electron in an interior orbit. The energy will be enough to knock the atomic electron out of the atom, which creates a vacancy in the corresponding energy state. Under such a condition, one of the electrons in the higher energy state (i.e., the one in an outer shell) falls down into the vacant energy state, which results in the emission of a photon.

The energy of the photon-emitted will be equal to the energy difference between the two states between which the atomic electron undergoes transition. These are the photons which give rise to the characteristic X-rays peaks.

Now the atomic energy level pattern is characteristic of the particular type of element to which the given atoms belong to. Hence the energy of the photons that formulate the X-ray peaks, depend on the type of the target material used, and is independent of the energy of the incident electrons, which in turn means that it is independent of the variation in applied high voltage V.

Energy Level Diagram or Understanding Characteristic Spectra in Terms of Bohr’s Theory

The origin of characteristic X-rays can be easily understood in terms of Bohr’s theory. The electrons producing X-rays are very energetic. These energetic electrons are capable of removing electrons even from the inner most K- or L-shel. When such an electron is removed, electron transition from the higher orbit occur. In accordance with Bohr’s theory, this results in the emission of (characteristic X-ray) photons.

The detailed structure of characteristic radiations can reasonably be well understood in terms of an energy level diagram Figure 10.14. In discussing the X-ray spectrum, we make the following assumptions:

1.The electrons with a particular value of n have (almost) identical energy.

2.The energy differences between the energy of the N-shell (n = 4) and the energy free electron can (almost) be neglected.

Let us suppose the impinging electrons remove a K electron. This vacancy can be filled up by an electron from either of L., M or N shells or a free electron. This possible transition can result in the Kα, Kβ line and the limiting line. The probability of Kα transition is maximum and hence the intensity of this line in K-series is more than the others. Similarly, radiations results when an election from the L shell (n = 2) is removed and the transitions results from higher orbits.

Moseley’s law

In 1913, Moseley carried out a systematic investigation of X-ray spectra of various elements. In his experimental observations, he found that, the frequencies of the Kα lines for various elements were proportional to the atomic numbers.

The actual relationship between the frequency v of a particular category of spectral
line, and the atomic number Z of the element which gives rise to the spectrum was given by Moseley as

v = a(Z – b)2

where, a and b are constants.

The relation is known as Moseley’s law which can

“The frequency of any particular category of spectral lines in the X-ray characteristic spectra of various elements, are proportional to the square of the atomic number of the element giving rise to the spectrum.”

The values of a and b vary slightly, when we change from Kα group of transition to Kβ group of transition, but Very significantly, when we change from one series to another, b is called screening constant. b has a value very nearly equal to unity for the K-series, but its value becomes equal to 7.4 for L-series.

If a graph of the frequency of a particular category of spectral lines, say Kα is plotted as function of the atomic number Z, then a straight line is obtained, as shown in Figure 10.15.


Let consider the case of K-series. The Moseley’s law, as applicable to Kα transitions is given

v = a(Z -1)2

Under normal conditions, there will be two electrons (Is electrons) in the K shell. These two electrons succeed in neutralizing two positive charges of the nucleus almost completely. As a result, the electrons in L shell feel as though the charge on the nucleus is only (Z – 2).

i.e., Zeff. = (Z – 2)

Now, the Kα transitions are due to the transition of electrons from the L shell to the K shell. These transitions can take place only when one of the S electrons is absent in the K shell neutralizes only one positive charge of the nucleus. As a result, the effective nuclear field at the L shell, preceeding the Kα transition will be

Zeff = (Z -1)

We know that, as per Bohr’s theory of Hydrogen atom, the frequency of radiation emitted a proportional to the square of the change on the nucleus.

Now, Since, Zeff = (Z -1), the frequency of the spectral line of Ka series are proportional to (Z-1)2. Similar explanation could be given to the frequencies of spectral lines of other series also.

Application/Importance of Moseley’s Law

The discovery of the property of X-ray spectral series led to a major improvement of Mendeleev’s periodic table. Four decade prior to Moseley’s work, Mendeleev’s had made the table of elements (the table known after his name), in order of the atomic weights. This table, as we know had remarkable successful in identifying the groups of elements, which had similar properties. But, the success was not without exceptions. For instance, cobalt and nickel with atomic weights of 58.93 and 58.71, were to be arranged in the reverse order, if they are to fit correctly in the groupings. The same problem was encountered in case of Argon and Potassium. The reason for the anomaly was not known.

The logical reasoning for such a discrepancy was provided, and the anomaly was removed, when in 1914, Moseley developed the concept of atomic number. Based on X-ray studies, he could evaluate the atomic numbers of various elements. Though, Moseley did not alter the periodic table, he fixed the positions of elements in exact places to which they fit into, naturally.

The conclusion of his work (which could be looked as applications) can be listed below

  • It is the atomic number, and not the atomic weight which determines the physical and chemical properties of an element.
  • It is the sequence of atomic number and not the atomic weight, which is to be followed in arranging the elements in the periodic table.
  • Moseley corrected the positions of Argon-Pottassium, Cobalt-Nickel, and Tellurium-Iodine in the periodic table.
  • It ruled out the possibility of discovery of any element would occupy a position in a-periodic table between two elements, whose atomic number varies by one. On the same count, it helps in predicting the existence of undiscovered elements. Following the same, the elements Celtium and Hafnium were discovered in the year 1914 and 1923.

Applications of X-rays
X-rays have wide applications in industries, scientific research, medical science engineering. Some of the important applications of X-rays are briefly mentioned below:

  • Industrial And Engineering Applications

i.            X-rays are used to detect detects in moulded materials like internal cracks in structures and also cavities formed in it.

ii.            Any weak points developed in welded joints and change in homogeneity of a dielectric material in electrical equipment can be detected by X-rays.

iii.            The structure of alloys can be studied.

  • Scientific Research Applications

i.            X-rays are used to study the complex structure of organic molecules, which gives useful information to understand biological processes.

ii.            X-rays are used to study the crystal structure of various materials, which is helpful in determining the electrical and mechanical behaviour of solids.

iii.            X-rays provide useful data regarding non-crystalline solids also which is useful in the study of their Physics,

  • Medical Applications

i.            Probably the greatest and immediate use of X-rays is in the medical field, since the X-ray photograph would instantaneously reveal the damage that have occurred inside the body in case of accident.

ii.            A controlled use of X-rays is helpful in treating cancer.

iii.            In fact, X-rays were used to determine structure of genes.

Bragg’s Law and Diffraction

Bragg’s Law refers to the simple equation

Nλ = 2d sin λ

derived by the English physicists Sir W.H. Bragg and his son Sir W.L. Bragg in 1913 to explain why the cleavage faces of crystals appear to reflect X-ray beams at certain angles of incidence (θ). The variable d is the distance between atomic layers in a crystal, and the variable λis the wavelength of the incident X-ray beam (applet) ; n is an integer.

This observation is an example of X-ray wave interference (Roentgenstrahlinter-ferenzen), commonly known as X-ray Diffraction (XRD), and was direct evidence for the periodic atomic structure of crystals postulated for several centuries. The Braggs were awarded the Nobel Prize in physics in 1915 for their work in determining crystal structures beginning with NaCl, ZnS and diamond. Although Bragg/ was used to explain the interference pattern of X-rays scattered by crystals, diffraction has been developed to study the structure of all states of matter with any beam, e.g., ions, electrons, neutrons, and protons with a wavelength similar to the distance between the atomic or molecular structures of interest.


Bragg’s Law can easily be derived by considering the conditions necessary to make the phases of the beams coincide when the incident angle equals and reflecting angle. The rays of the incident beam are always in phase and parallel up to the point at which the top beam strikes the top layer at atom z (Figure 10.16). The second beam continues to the next layer where it is scattered by atom B. The second beam must travel the extra distance AB + BC if the two beams are to continue traveling adjacent and parallel. This extra distance must be an integral (n) multiple of the wavelength (λ) for the phases of the two beams to be the same.

Nλ = AB + BC                                                                                                              … (2)

FIGURE 10.16 Deriving Bragg’s Law using the reflection geometry and applying trigonometry. The lower beam must travel the extra distance (AB + BC) to continue travelling parallel and adjacent to the top beam.

Recognizing d as the hypotenuse of the right triangle ABz, we can use trigonometry to relate d and θ to the distance (AB + BC). The distance AB is opposite θ so,

AB = d sin θ                                                               … (3)

Because AB = BC equation (2) becomes,

n λ = 2AB                                                                     … (4)

Substituting eq. (3) in equation (4) we have

n λ = 2 d sin θ

and Bragg’s Law has been derived. The location of the surface does not change the derivation