section_path: Characteristics/Motion and energy
section_name: Motion and energy
paragraph_text: Motion and energy
  
  According to Einstein's theory of special relativity, as an electron's speed approaches the speed of light, from an observer's point of view its relativistic mass increases, thereby making it more and more difficult to accelerate it from within the observer's frame of reference. The speed of an electron can approach, but never reach, the speed of light in vacuum, c. However, when relativistic electrons—that is, electrons moving at a speed close to c —are injected into a dielectric medium such as water, where the local speed of light is significantly less than c, the electrons temporarily travel faster than light in the medium. As they interact with the medium, they generate a faint light called Cherenkov radiation.
  
  The effects of special relativity are based on a quantity known as the Lorentz factor, defined as γ = 1 / 1 − v 2 / c 2 {\displaystyle \scriptstyle \gamma =1/{\sqrt {1-{v^{2}}/{c^{2}}}}} where v is the speed of the particle. The kinetic energy K of an electron moving with velocity v is:
  
  where m is the mass of electron. For example, the Stanford linear accelerator can accelerate an electron to roughly 51 GeV. Since an electron behaves as a wave, at a given velocity it has a characteristic de Broglie wavelength. This is given by λ = h / p where h is the Planck constant and p is the momentum. For the 51 GeV electron above, the wavelength is about 2.4 × 10 m, small enough to explore structures well below the size of an atomic nucleus.