Answer to Question #2357 Submitted to "Ask the Experts"

X rays, which originate in the electron cloud around the nucleus of an atom, are electromagnetic radiations like gamma rays, light, radio waves, etc. The wavelength of any electromagnetic wave can be calculated from the de Broglie wave equations,

ν (frequency of wave) = E (energy)/h (Planck's constant),

where Planck's constant is 6.6256 × 10^-27 erg • s. From basic physics, the relationship between the wavelength of a photon, or a quantum of electromagnetic energy, and its frequency is

λ (wavelength) = c (speed of light)/ν (frequency of wave),

where the speed of light in a vacuum is approximately 3 × 10¹⁰ cm s^-1. To complete the conversion, the electron volt (eV) is equal to 1.6 × 10^-12 erg.

For example, the wavelength of an x-ray photon of energy 120 kV, or 1.20 × 10⁵ eV, is

λ = c • h/E,

λ = (3 × 10¹⁰ cm s^-1) • (6.6256 × 10^-27 erg • s)/(1.2 × 10⁵ eV) • (1.6 × 10^-12 erg eV^-1), and

λ = 1.04 × 10^-9 cm

In medicine, x-ray energies run from about 15 kVp for mammography to more than 20 MV in radiation therapy. Thus, the wavelengths will correspond to 8.3 × 10^-9 cm to 6.2 × 10^-12 cm, respectively.

It should be noted that the x rays used in medicine are produced by the bremsstrahlung interaction of high-energy electrons in a metal target. A broad range of x rays is produced, from very low energies of only a couple of eV to the maximum energy of the incident electrons that strike the target. The convention is to list the maximum or peak x-ray energy that can be produced by the incident as kVp. In therapy, the convention is to use the unit of MV.

John P. Jacobus, MS
Certified Health Physicist