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Physics Tutorial: Photons and X-Rays

When Wilhelm Roentgen invented X-ray technology in 1895, medical science took a big leap. Doctors were now able to easily see broken bones, swallowed objects, and tooth decay. And today, modified X-rays can be used to see soft tissue as well.

Inside X-ray machine is a tube in which a target (anode) made of heavy atoms, such as tungsten** is shot at by an electron gun (cathode) which sends high energy electrons to the target. Electrons are deflected and Voila! x-rays are produced. Because electrons are shot at a target and energy is released, making X-rays is like the photoelectric effect in reverse.

X-Rays are carried by photons* like any other form of electromagnetic radiation***. We can't see them because, unlike light, our eyes are not sensitive to the shorter wavelength of X-rays.

There are two ways to make X-ray photons:

• Bremsstrahlung: Some of the electrons shot at the target are drawn toward the nucleus of the metal

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  atoms. and because the nucleus is positive and the electrons are negative, the electrons are deflected. The electrons loses energy because of the deflection and the energy is lost in the form of an X-ray.

• K-Shell: This produces higher intensity X-rays than Bremsstrahlung and is more common. In atoms electrons are arranged in shells of energy and the k-shell is the lowest and the nearest to the nucleus. An electron shot at the electron in the k-shell provides enough energy to knock the electron out of its energy state. The vacancy in the k-shell gives room for a higher energy electron from the tungsten to fall into place so an electron from the next shell comes and sheds energy as it falls into place. The energy is emitted in the form of x-ray photons. As you might think, this starts a cycle where electrons from outer (and higher energy) shells of the atom keep coming in to try and fill the voids. They also keep shedding energy to do this, consequently emitting X-rays.

All of the collisions in the tube make the machine very hot so a motor rotates the anode to keep it cool. Lead covers the whole machine to keep the radiation from going everywhere. There is a small window in the lead though, that lets a beam of the X-ray photons escape. On the other side of the patient a camera records the pattern of the x-rays that pass through the body. The camera is just like any normal film camera, except X-ray light sets it off instead of visible light.


When a high energy X-ray photon collides with an electron, the Compton effect occurs. The photon and the

electron are deflected at an angle, and because the photon transferred some energy to the electron, the photon comes out of the collision with a longer wavelength. The longer the wavelength, the bigger the angle. Compton scattering is what we call the collisions and the change of wavelength. The Compton effect usually occurs with high energy X-rays and low atomic numbers.

Moseley**** did a lot of work with X-rays, but here's one equation of his is used to find frequency of x-rays from the L-shell:

• v = (5/36)cR(Z - 1)²
  

• v (nu) is the frequency measured in hertz

• c is the speed of light equal to 2.998x10⁸m/s

• R is the Rydberg constant equal to 1.09768x10⁷m^-1

• Z is the atomic number (number of protons in the nucleus)

For more from Moseley read his publication which is linked at the bottom of the page.

Let's try a problem using this equation. An X-ray machine uses the k-shell technique to produce X-rays. It's target is made of tungsten (W). What is the frequency of the X-rays emitted from the L-shell? v = (5/36)cR(Z - 1)²
v = (5/36)(2.998x10⁸)(1.09768x10⁷)(74-1)²
v = 2.44x10¹⁸Hz

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Elona Turley