X-ray Photon Energy and X-ray Tube Voltage

Electrons can give all of their kinetic energy to a single photon when they strike the anode of a CRT. (This is something like the photoelectric effect in reverse.) The kinetic energy of the electron comes from electrical potential energy. Thus we can simply equate the maximum photon energy to the electrical potential energy—that is, $\text{hf}=\text{qV.}$ (We do not have to calculate each step from beginning to end if we know that all of the starting energy $\text{qV}$ is converted to the final form $\text{hf.}$)

The maximum photon energy is $\text{hf}=\text{qV}$, where $\text{q}$ is the charge of the electron and $\text{V}$ is the accelerating voltage. Thus,

From the definition of the electron volt, we know $\text{1 eV}=\text{1}\text{.}\text{60}\times {\text{10}}^{\text{–19}}\text{J}$, where $\text{1 J}=\mathrm{1\; C}\cdot \mathrm{V.}$ Gathering factors and converting energy to eV yields

This example produces a result that can be applied to many similar situations. If you accelerate a single elementary charge, like that of an electron, through a potential given in volts, then its energy in eV has the same numerical value. Thus a 50.0-kV potential generates 50.0 keV electrons, which in turn can produce photons with a maximum energy of 50 keV. Similarly, a 100-kV potential in an x-ray tube can generate up to 100-keV x-ray photons. Many x-ray tubes have adjustable voltages so that various energy x rays with differing energies, and therefore differing abilities to penetrate, can be generated.