# X-Ray Properties (Energy, Wavelength, Inverse Square Law) For Radiologic Technologists

Basics of x-ray properties for radiographers and radiologic technologists include: wave and particle models for x-rays, relationships between Energy, wavelength and frequency, and 1/R^2 effect.

Radiation is energy emitted/transmitted as a wave or particle that travels through a medium (such as the air or a patient). A brief comparison of the different types of radiation is given here in the table.

# Basic X-Ray properties

## X-Rays Similarities and Differences with Visible Light

The x-rays that are produced by diagnostic x-ray equipment have a lot in common with the visible light that we are all very familiar with. As children we all learned about ROYGBIV, which are the different colors of light in order from lowest energy to highest energy (also the longest wavelength to shortest wavelength, more on that to come).

This visible light is just a small portion of all the electromagnetic radiation. The spectrum of electromagnetic waves changes gradually from lowest energy (radio waves and microwaves) to the highest energies (x-rays and gamma rays).

At the bottom of this figure there is a schematic which shows the whole electromagnetic spectrum. On the left of the figure are the lowest wavelengths (highest energies). On the right of the figure are the highest wavelengths (lowest energies).

X-Rays, used for diagnostic imaging in CT scanners, have average energy around 60 keV which is 10,000 times higher than the energy of regular light we see around us.

So, x-rays are electromagnetic radiation just like the light around us but with much higher energy.

Because x-rays have much higher they have shorter wavelength. Since their wavelength is so short in most scenarios we can treat x-rays like particles traveling through space (i.e. just ignore the fact that they are really waves). We call each of these individual packets x-ray photons.

Rad Take-home Point: X-rays are part of the electromagnetic spectrum just like visible light. X-rays can be treated as wave or particles (photons) since their wavelengths are so short.

## Wave Properties

As we mentioned above x-rays can be treated like waves or particles, and therefore for completeness we want to describe the wave characteristics of x-rays. X-rays are alternating electric and magnetic waves that are traveling in perpendicular planes. But to make things simpler in the figures we will draw just a single wave as that is easier to visualize.

Electromagnetic waves have fundamental properties – repeating peaks and valleys with certain: amplitude and a frequency (directly related to the Energy, and inversely related to the wavelength).

The waves repeat and the distance for the wavelength to repeat. Therefore, the distance from one valley to the next valley is the wavelength. Likewise, the distance from one peak to the next peak is also the wavelength.

The plots in the wave figure show the height or amplitude of the wave as a function of time. The number of times that the wave pattern repeats in a given time is called the frequency (ν). So, longer wavelengths have lower frequencies because they have less peaks in a given time.

Energy of x-rays depends directly on its frequency (E~f) and inversely related to wavelength (E~1/λ). Electromagnetic waves with higher frequencies have proportionally higher energies.

What if we compare the two waves and ask which has the higher energy? The wave with the shorter wavelength, will have higher frequency. Since we know that the energy scales directly with the frequency we know that the wave that has the shorter wavelength will have higher energy.

For instance, violet light has a shorter wavelength than red light and thus violet light has higher energy. Likewise, a 60keV x-ray photon and a 30 keV x-ray photon have the same relationship where the wavelength of the 60keV x-ray is smaller. The same principles apply when comparing electromagnetic radiation at different parts of the spectrum.

Rad Take-Home Point: Waves with shorter wavelengths oscillate more in a given time and have a higher frequancy  (f ~1/λ) and a higher energy (E~f and E~1/λ).

## Inverse Square Law

If you are familiar with light being much more intense by a light bulb or heat being much hotter right near a fire this is because of the inverse square law.

The number of x-ray photons that pass through a given point depends on distance between source and detector. If we think about the fact that x-rays travel straight lines like particles, they will spread out more with greater distances.

The name for this effect is a divergent x-ray beam coming from the x-ray tube.

In the figure we can see that the density of x-rays much higher closer to the source and is weaker further from the source and it is proportional of square of the distance x-ray quantity ~ 1/r2.

For example, if we increase the distance three times between source and detector the strength of beam will decrease nine times.

This is an important thing to consider when you are setting up the technical parameters on x-ray system.  The distance is very important in terms of the fluence of x-rays (number of x-rays in a given time) which are going to be incident on the detector.

Rad Take-home Point: X-rays travel in straight lines and the closer you are to the source the greater the number of x-rays passing through (~ 1/r2).

## Primary vs Remnant Beam (Impact of Patient on Radiation)

The description above is a very high level description of wave properties. Now, we come back to diagnostic x-ray and discuss how the x-ray spectrum is different after passing through the body.

In our post on x-ray generation we discussed how x-rays are generated and the fact that the x-rays coming out of an x-ray tube are from many different energies. The plot of the x-ray energies is called the x-ray spectrum.

In describing the x-ray spectrum multiple terms are used include quality of the x-ray beam and quantity of x-rays in the beam.

If two x-ray spectra have different shapes they are said to have different x-ray quality.

If two spectra have the same shape but different heights they have different quantity but the same quality.

In our post on  x-ray interactions we discussed that in the diagnostic energies the low energy x-rays are more likely to be stopped within the body.

The exit spectrum or remnant spectrum after it passes through the body with have a different quality than the incoming spectrum. The remnant x-ray beam will have fewer low energy x-rays as they are more likely to be stopped in the body.

If the x-ray tube is set to have 140 kvP, highest energy x-ray photons can came out with an energy of 140 keV. There will also be a number of lower energy photons as in the figure. Since the lower energy photons stop in the body at a higher rate the spectrum coming out of the patent is shifted to the right or harder.

On the other hand, beam quality does not depend on the tube current (mA) but the beam quantity depends on mA.

The size of patient’s body may cause significant attenuation of x-rays and affects the energy distribution of x-rays leaving the patient.

Rad Take-home Point: The remnant (exit) x-ray is harder than the incoming spectrum due to the low energy photons being more likely to be stopped in the patient.

## Other Fundamental X-Ray Properties

We add references to a couple of topics on x-rays that are covered in much more depth on other pages here at How Radiology Works.

When travelling through the body of the patient, Photoelectric and Compton interactions of x-rays with matter takes place (see our post on x-ray interactions). This process means x-rays are knocking out electrons from the matter, ionizing (removing electrons) and releasing energetic electrons near the bodies DNA (which can cause damage). So, it is important to consider carefully the patient radiation dose in each case.

In our post on radiation biology we describe the mechanisms for radiation damage to the body.

Rad Take-home Point: In addition to generating diagnostic x-ray images, x-rays can cause damage to human tissue and the radiation dose should be made as low as reasonable possible for each diagnostic task.

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