What is meant by boiling off electrons in a heater coil? In my electricity and magnetism course, we used a Thompson tube to produce an electron beam. There is a heating element at the back of the tube and the lab manual claims that "electrons are boiled off." Can someone explain what is meant by this? Boiled off seems an odd term to use but maybe if I understand it meaning, it won't seem so odd. 
 A: The heated filament produces electrons by thermionic emission.
It takes energy to remove an electron from a metal surface, and this energy is called the work function. In a metal the electrons are continuously scattering off lattice vibrations, i.e. the vibration of the metal atoms due to thermal energy. Typically the energy the electron gains from the scattering is of order $kT$, where $k$ is Boltzmann's constant and $T$ is the temperature. At room temperature $kT$ is about 0.025eV while metal work functions are generally around 2 - 5eV, so it would appear that electrons aren't scattered with enough energy to escape the metal.
However the scattering is a random process, and occasionally an electron will be scattered with an energy greater than the work function. If this electron is near the metal surface it can escape. At room temperature this is very unlikely, but as you heat the metal the energy of the lattice vibrations increases and consequently the electrons are scattered with greater energy. At some point the scattering energy gets big enough that a significant number of electrons are emitted, and this is thermionic emission.
It's important to remember that the probability that an electron is scattered with enough energy to escape the metal remains small even when the metal is red hot. Only a very small percentage of the electrons in the metal escape, but this small escape rate is enough to generate a measurable current.
Anyhow, you can see why electrons are described as being boiled off, because it's the thermal vibrations of the metal that eject the electrons.
