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Laws of photoelectric emission

For a given metal and frequency of incident radiation, the rate at which photoelectrons are ejected is directly proportional to the intensity of the incident light.
For a given metal, there exists a certain minimum frequency of incident radiation below which no photoelectrons can be emitted. This frequency is called the threshold frequency.
Above the threshold frequency, the maximum kinetic energy of the emitted photoelectron is independent of the intensity of the incident light but depends on the frequency of the incident light.
The time lag between the incidence of radiation and the emission of a photoelectron is very small, less than 10^-9 seconds.

Equations

In analysing the photoelectric effect quantitatively using Einstein's method, the following equivalent equations are used:

Energy of photon = Energy needed to remove an electron + Kinetic energy of the emitted electron

Algebraically:

$hf = phi + E_{k_{max}} ,$

where

h is Planck's constant,
f is the frequency of the incident photon,
$phi = h f_0$ is the work function (sometimes denoted $W$ instead), the minimum energy required to remove a delocalised electron from the surface of any given metal,
$E_{k_{max}} = rac{1}{2} m v_m^2$ is the maximum kinetic energy of ejected electrons,
f₀ is the threshold frequency for the photoelectric effect to occur,
m is the rest mass of the ejected electron, and
$v m$ is the velocity of the ejected electron.

Note: If the photon's energy (hf) is less than or equal to the work function (

?

), no electron will be emitted. The work function is sometimes denoted

W

.

Since an emitted electron cannot have negative kinetic energy, the equation implies that if the photon's energy is less than the work function, no electron will be emitted.

According to Einstein's special theory of relativity the relation between energy (E) and momentum (p) of a particle is $E = sqrt{(pc)^2 + (mc^2)^2}$ , where m is the rest mass of the particle and c is the velocity of light in a vacuum.

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Laws of photoelectric emission

Equations