For the photoelectric effect, the maximum kinetic energy \( E_k \) of the photoelectrons is plotted against the frequency \( \nu \) of the incident photons as shown in figure. The slope of the graph gives
The photoelectric effect is described by the equation:
\[
E_k = hf - \phi
\]
where:
- \( E_k \) is the kinetic energy of the emitted electrons,
- \( h \) is Planck’s constant,
- \( f \) is the frequency of the incident photons,
- \( \phi \) is the work function of the metal.
When the equation is rearranged in the form of \( y = mx + b \):
\[
E_k = hf - \phi,
\]
where:
- \( E_k \) corresponds to \( y \),
- \( f \) corresponds to \( x \),
- \( h \) (Planck’s constant) is the slope \( m \),
- \( -\phi \) is the y-intercept.
Thus, the slope of the graph, which represents the relationship between kinetic energy and frequency, gives Planck’s constant \( h \).
When light shines on a metal, electrons can be ejected from the surface of the metal in a phenomenon known as the photoelectric effect. This process is also often referred to as photoemission, and the electrons that are ejected from the metal are called photoelectrons.
Photoelectric Effect Formula:
According to Einstein’s explanation of the photoelectric effect :
The energy of photon = energy needed to remove an electron + kinetic energy of the emitted electron
i.e. hν = W + E
Where,
h is Planck’s constant.
ν is the frequency of the incident photon.
W is a work function.
E is the maximum kinetic energy of ejected electrons: 1/2 mv².
Laws of Photoelectric Effect:
The photoelectric current is in direct proportion to the intensity of light, for a light of any given frequency; (γ > γ Th).
There exists a certain minimum (energy) frequency for a given material, called threshold frequency, below which the discharge of photoelectrons stops completely, irrespective of how high the intensity of incident light is.
The maximum kinetic energy of the photoelectrons increases with the increase in the frequency (provided frequency γ > γ Th exceeds the threshold limit) of the incident light. The maximum kinetic energy is free from the intensity of light.
The process of photo-emission is an instantaneous process.
