Final answer:
The velocity of an electron emitted from a metallic surface by a photon is a result of the photoelectric effect, where photons eject electrons by transferring energy that exceeds the metal's work function, converting it into the electron's kinetic energy.
Step-by-step explanation:
The phenomenon you are referring to is called the photoelectric effect, which occurs when photons illuminate a metallic surface and have enough energy to eject electrons from that surface. According to Einstein's explanation of this effect, light can be thought of as consisting of particles known as photons.
When a photon with sufficient energy collides with an electron, the electron absorbs the photon's energy and may be ejected from the metal surface if this energy exceeds the metal's work function, the minimum energy required to remove an electron from the metal.
The kinetic energy of the ejected electron is determined by subtracting the work function of the metal from the energy of the photon. If the photon's energy is greater than the work function, the surplus energy becomes the kinetic energy of the ejected electron, and we can observe this as the electron's velocity.
The relationship between the energy of the photon (which is quantized and dependent on the light's frequency) and the kinetic energy of the ejected electron is a cornerstone of quantum mechanics and illustrates the particle nature of light.