Question

Write Einstein’s photoelectric equation. State clearly how this equation is obtained using the photon picture of electromagnetic radiation.
Write the three salient features observed in photoelectric effect which can be explained using this equation.

Answer 1

Hint: Study about the wave nature and the particle nature of light. Imagine how they are different. Try to solve this photoelectric effect using both wave and particle nature. Only the particle nature of light is suitable for this phenomenon. Obtain the equation using the concepts of photoelectric effect.

Complete Step-by-Step solution:
The photoelectric effect is a phenomenon where electrons from the surface of a metal are emitted by absorbing light.
When a light of sufficient energy is incident on a metal surface, the electrons on the surface of the metals absorb this light and emitted out of the surface of the metal.
According to the wave theory of light, light is a form of wave which propagates through space. But it cannot explain the photoelectric effect.
Einstein introduced the particle theory of light. Where he explained that light is a particle called a photon. The energy carried by each particle of light called photon depends on the frequency as,
$E=h\nu $
Where h is the Planck’s constant with value, $h=6.626\times {{10}^{-34}}Js$
When a photon with sufficient energy is incident on the metal surface the electron absorbs the energy. With energy required to eject the electron the electron is emitted and the rest of the energy is converted to the kinetic energy of the electro.
So, we can write,
$\text{energy of photon = energy required to eject the electron + kinetic energy of the ejected electron}$
$E=W+K.E.$
Where, W is the work function or the threshold energy below which photoelectric effect is not possible
$E=h{{\nu }_{0}}+\dfrac{1}{2}{{m}_{e}}{{v}^{2}}$
The kinetic energy of the photoelectron is given by,
$K.E.=E-h{{\nu }_{0}}$
Where, ${{\nu }_{0}}$ is the threshold frequency.
Stopping potential of the photoelectron is equal to its kinetic energy.
Three salient features of photoelectric effect are,
1. Maximum kinetic energy of the emitted photoelectrons depends on the frequency of the light incident on the surface. With increase in the frequency, kinetic energy of the photoelectron will increase linearly.
2. No photoelectric effect is possible below threshold energy. Below this energy electron will not have sufficient energy to be ejected out of the surface.
3. With this phenomenon we can explain the particle picture of light where light is assumed to consist of particles with energy which is dependent on its frequency.

Note: The opposite of photoelectric effect is also possible. When we have a beam of fast-moving electrons near any positively charged metal surface, it can absorb the electron emitting light of certain wavelength. This is called inverse photoelectric effect.