Note-A-Rific: X-Rays

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Uses of X-rays

X-Rays, which were discovered by Wilhelm K. Roentgen, have several uses…

• They are now most commonly used as a diagnostic tool to make x-ray images.
• In some cases they are used to fight some types of cancer.
• They are also used to study the crystal structure of solids, since their wavelength is about the same size as the spacing between atoms.
• Unfortunately, X-Rays have high enough energies that they can damage and destroy living tissue, so exposure to them must be limited.

Producing X-Rays

X-Rays are produced when accelerated electrons strike a (typically) metal target.

• They can collide with atoms of the material giving up most of their energy as heat (about 99%, so x-ray tubes must be cooled.) and the rest as a photon

• The electrons sometimes slam right into the atoms of the material and throw off the x-rays.
• Sometimes the electrons just “skid” past the atoms, moving in a curve…
• Since any curved motion is an acceleration, the electron in this case is undergoing negative acceleration called Bremsstrahlung (German for “Braking Radiation”)
• Since Bremsstrahlung does not convert as much energy into x-rays (it never hit anything), these x-rays have higher wavelengths (lower frequency à lower energy)

An electron might give up some or all of its radiation in one of these collisions / skids…

A graph of the x-ray intensity versus wavelength for a Molybdenum target is roughly sketched out here:

Minimum Wavelength (λ_O): Since f = 1/ λ , the shortest possible wavelength of x-ray that can be emitted is at the highest possible frequency. That means that it must be the one with the most energy, that the electron transferred all its energy to the photon. This is the wavelength that we will be calculating soon, since it’s easy for us to assume that all the energy is transferred to the photon, instead of guessing “Oh, I think only 45% transferred this time.” This value depends on how fast the electron was moving.

Characteristic Lines: The two sharp peaks in blue and orange on the graph are referred to as characteristic lines or characteristic x-rays. You can think of this as the fingerprint of whatever material the electrons are hitting, as all materials have different characteristic lines. The reason for this is because they depend on the structure of the electrons in the material’s atoms, and every element has a unique atom configuration.

Bremsstrahlung: The braking radiation happens at the end of the graph at long wavelengths. We expect this since bremsstrahlung involves a slowing of the electron without completely stopping it. The electron only transfers some of its energy to a low energy, low frequency photon.

Calculating Minimum Wavelength (λ_O)

We assume that all of the electron’s kinetic energy is changing into the x-ray photon…

In the formula you are used to using there is a “q” for charge. Since we are always using electrons (an elementary charge) I’ve subbed in “e”.

E_k = e V           E = h ¦_o ¦ = c/l_o

e V = h ¦_o

Example: What is the shortest wavelength x-ray photon emitted in an x-ray tube subjected to 5.0 x 10⁴V?

Remember, it is an electron’s charge we use in “e”.

 =

l_o = 2.5 x 10^-11m

            Or about 0.025nm, which agrees well with experiment.

This is a very common type of question on diploma exams, but you will need to know how to quickly derive the formula from the ones that are on your data sheet.