Threshold Frequency, Work Function and the Laws of Photoelectric Emission

Work function. The work function of a metal, denoted $\phi_0$, is defined as the minimum energy that must be supplied to free the most loosely bound electron from the surface of that metal and remove it completely, against the attractive forces holding it inside the metal. It is a property of the metal (and, to a lesser extent, of the condition and cleanliness of its surface), and is conventionally quoted in electron-volts (eV), since the energies involved are of the same order as the energy an electron gains crossing a potential difference of a few volts. This section's table lists approximate work-function values for several common metals -- alkali metals such as caesium and potassium have particularly LOW work functions (easiest to eject an electron from), which is exactly why they are the practical choice for photocells and photomultiplier tubes meant to respond to ordinary visible light.

Threshold frequency and threshold wavelength. For a given metal, the threshold frequency $\nu_0$ is the minimum frequency of incident electromagnetic radiation that can, in principle, just barely eject a photoelectron from that metal's surface; light of any LOWER frequency, however intense, produces no photoelectric emission at all. Once Einstein's equation is available (Section 11.7), the threshold frequency is seen to be fixed directly by the work function, $\nu_0=\phi_0/h$. The corresponding threshold wavelength, the LONGEST wavelength of light capable of causing emission, follows from $c=\nu\lambda$:

The laws of photoelectric emission (a formal summary of Section 11.3's findings). Bringing together everything Lenard's apparatus established, the experimentally observed laws of photoelectric emission are:

1. For light of a fixed frequency (above the threshold frequency of the given metal), the photoelectric current -- and hence the number of photoelectrons emitted per second -- is directly proportional to the intensity of the incident light.
2. For a given metal, the maximum kinetic energy of the emitted photoelectrons depends only on the FREQUENCY of the incident light (increasing linearly with it, Section 11.4's second graph), and is completely independent of the light's intensity.
3. There is a definite threshold frequency $\nu_0$, characteristic of each metal, below which no photoelectric emission takes place at all, no matter how great the intensity of the incident light or how long it is allowed to shine. …