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# X-ray spectrum

## X-rays

X-rays are a form of electromagnetic radiation which have wavelengths ranging from $0.01\text{nm}$ to $10\text{ nm}$.

Different wavelengths of X-rays emitted during X-ray production collectively form an X-ray spectrum and are normally represented as a graph of intensity versus wavelength.

The analysis of X-ray spectra led to the discovery that electrons in an atom have discrete energy levels.

X-ray radiograph of two human elbows. X-rays are energetic enough to penetrate human flesh but is absorbed by bone.

## Intensity spikes

The X-ray spectrum is produced by two distinct processes which can be explained using the quantum theory of energy.

Intensity spikes (marked as $K_{\alpha}$ and $K_{\beta}$) are produced when excited metal atoms in an X-ray tube return to their ground state. These atoms are excited by collisions with the accelerated electrons in the X-ray tube.

This produces X-ray photons with discrete energies corresponding to the two wavelength peaks. The wavelength of the X-ray photons depends only on the metal used in the X-ray tube.

## Continuous spectrum and bremsstrahlung

The continuous spectrum in the background of an X-ray spectrum is caused by electron bremsstrahlung (German for braking/decelerating radiation).

The electrons which are accelerated into the metal target are deflected from their initial path by the positively charged nuclei of the metal atoms.

This causes the electrons to decelerate and lose energy in form of emitted photons without exciting any atoms.

The energy loss of the electrons and the corresponding wavelengths of the emitted photons are variable. The radiation comprised of these photons forms a continuous spectrum.

## Minimum wavelength of the continuous spectrum

It can be observed that the continuous spectrum has a minimum wavelength. This minimum value occurs when all of the kinetic energy of an electron is converted into a bremsstrahlung photon.

The minimum wavelength $(\lambda_{\text{min}})$ is given by: $$hf=h\left(\frac{c}{\lambda_{\text{min}}}\right)=\frac{1}{2}mv^{2}$$ $hf$ is the energy of the bremsstrahlung photon, $c$ is the speed of light, $m$ is the mass of an electron and $v$ is the speed of the electron.