X-Ray

Definition

X-radiation (composed of X-rays) is a form of electromagnetic radiation with photon energies between \( 100 \,\, eV \) and a few \( MeV \), corresponding to wavelengths between \( 10^{−8} \) and \( 10^{−12} \,\, m \).

Bremsstrahlung

The acceleration or deceleration of electric charges generates electromagnetic radiation, which is called Bremsstrahlung. The frequency of this radiation is greater, the more the charges are accelerated. If electrons with great speed and thus large kinetic energy (several \( keV \)) crash on a metal, they are decelerated abruptly. The result is Bremsstrahlung of high energy whose frequency is in the X-ray range.

X-ray tube

The following animation shows a X-ray tube which is used for generating X-radiation.

An einer Kathode wird eine Heizspannung \( U_H \) angelegt, wodurch Elektronen aus der Glühwendel herausgelöst werden und durch die Beschleunigungsspannung \( U_B \) in Richtung der Metallanode beschleunigt werden. At a cathode a heating voltage \( U_H \) is applied, whereby electrons are removed from the filament and are accelerated towards the anode metal through the accelerating voltage \( U_B \).

\( U_B = \) -1 \(   kV\)
\( U_H = \) -1 \(   V\)
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When an electron hits the anode a photon is created, to which a part of the kinetic energy of the electron is transferred. The remaining energy heats the anode.

The photon energy thus depends on how much energy the photon is transferred and is different for each impact. The maximum photon energy is obtained when the total kinetic energy is transferred to a photon:

$$ E_{max} = E_{kin} = e \cdot U_B $$

As you can see, the maximum energy is proportional to the acceleration voltage \( U_B \), since this is decisive for the speed and therefore the kinetic energy of the electrons.

The greater the heating voltage, the more electrons are released from the filament and the higher the intensity of the radiation.

Duane–Hunt law: When we know the maximum energy we can determine the maximum frequency (cutoff frequency) \( F_g \) and the minimum wavelength \( \lambda_G \) (cutoff wavelength) of the resulting X-rays:

$$ f_G = \dfrac{E_{max}}{h} = \dfrac{e \cdot U_B}{h} $$ $$ \lambda_G = \dfrac{c \cdot h}{E_{max}} = \dfrac{c \cdot h}{e \cdot U_B} $$

One can summarize the three formulas:

$$ E_{max} = e \cdot U_B = h \cdot f_G = h \cdot \dfrac{c}{\lambda_G} $$

Spectrum of the X-radiation

The following \( I(E_{Ph}) \) chart shows the relative intensity of photon energies of X-ray tube with molybdenum as anode metal.

Bremsspectrum     Characteristic spectrum     X-ray spectrum    

The X-ray spectrum is composed of two sub-spectra, caused by different processes.

The X-ray radiation, which is caused by the deceleration of electrons, known as Bremsspectrum (or continuous spectrum) is the basis of the X-ray spectrum.

However, there is still another process that causes X-ray radiation. It is responsible for the so-called characteristic spectrum, which peaks at \( E_1 = 17,4   keV \) and \( E_2 =   19,6 keV \).

Characteristic x-ray

In the following animation you can see the core and the shell of a magnesium atom using the Bohr model. The electrons move in circular orbits (called shells) around the core.

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The X-rays are created is as follows:

  • A free electron collides with a bound electron on an inner shell of the atom. Its energy is transferred to the bound electron. If this energy is greater than the nuclear binding energy of the atom, the bound electron is emitted from the atomic shell. Otherwise, the energy is often enough for the electron to move to a more distant shell. In both cases there is a gap on the inner shell of the atom.
  • An electron from an outer shell now changes to the inner shell to fill the resulting gap. Since the electrons in the outer shells have higher energy, this energy is released.
  • This energy difference is typically in the range of \( 1 - 100 \,\, keV \), and is therefore emitted as X-rays. Thus, the radiation has the energy difference between a higher (e.g. L) and low (for example, K) shell. Because the energy differences between the shells for each element are different, the most immediate radiation is element-specific. Therefore, the X-ray radiation called "characteristic X-rays".

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