# Explanation of Photoelectric effect by Einstein equation

Albert Einstein won the Nobel Prize in 1905 for his explanation of Photoelectric effect. There were some failures of classical mechanics to explain this phenomenon. Then Einstein explained it on the basis of quantum theory. In this article, we are going to explore the definition and properties of Photoelectric effect explained by Einstein and will derive Einstein’s equation of photoelectric effect.

• What is Photoelectric effect?
• Definition of photoelectric current
• Some important terms of photoelectric effect – Work function, Cut-in frequency, Stopping potential
• Properties of Photoelectric effect
• Explanation of photoelectric effect by Einstein
• Einstein’s equation of photoelectric effect
• Applications of photoelectric effect

## What is Photoelectric effect?

If the light of sufficient frequency (or energy) is incident on a metal surface, electrons emit from the metal after absorbing the energy of the incident light. If a proper circuit arrangement is made, an electric current flows through the circuit due to the emission and then the motion of the electrons.

This phenomenon of emission of electrons after absorbing the energy of electromagnetic radiation or light is known as the Photoelectric effect and the rate of the flow of the photoelectrons through the circuit arrangement is called the Photocurrent. This process transfers the energy of photons into the kinetic energy of electrons.

Photoelectric effect is the evidence or the proof of the particle nature of light. In quantum mechanics, Max Planck said that the energy of light is discrete. While explaining the Photoelectric effect Einstein named each quantum energy of light a Photon.

## Definition of photoelectric current

The Photoelectric current is defined as the rate of the flow of photoelectrons through a circuit arrangement. It is similar to the conduction current. But the origin of photocurrent is different from the conduction current.

## Some important terms related to Photoelectric effect

#### Work functionof metal

The minimum energy required to remove an electron from the surface of a substance is known as the work function of the substance. Work function depends on the nature of the substance. The alkali metals like Sodium (Na), Potassium (K), etc. have lower work function. It is very easy to remove electrons from the surface of the metal having a lower work function.

#### Cut-in frequency or Threshold frequency

The Threshold frequency is the minimum frequency of the incident light that can emit electrons from the metal surface. The light with a frequency below the threshold frequency does not have enough energy to remove an electron from the metal surface.

#### Stopping Potential

If a negative potential difference of anode or plate with respect to the cathode is applied the photocurrent reduces. At a certain value of negative potential, the photocurrent becomes zero. The negative potential of the anode with respect to the cathode for which the photocurrent becomes zero or the photoelectric effect stops is called the Stopping potential.

## Properties of Photoelectric effect

The characteristics of Photoelectric effect are as followings –

1. Photoelectric effect is an instantaneous process. It starts as soon as the light of sufficient frequency is incident on the metal surface.
2. Only the light of frequency above the threshold frequency can emit electrons from metal surface. That means the incident light must have an energy greater than the work function of the metal. Now, different metals have different work functions. Thus, the threshold frequencies of light incident on different metals are also different.
3. The number of emitted electrons or the photocurrent is independent of the frequency of incident light. But photocurrent is directly proportional to the intensity of light i.e. the number of incident photons per unit area per unit time.
4. The kinetic energy of emitted electrons is directly proportional to the frequency of incident light.
5. The emission of electrons in the Photoelectric effect is independent of the temperature of the metal surface.

## Explanation of photoelectric effect by Einsteinusing Quantum theory

Albert Einstein explained the Photoelectric effect from the point of view of Quantum mechanics. He explained it as followings –

1. In Photoelectric effect, light shows its particle nature i.e. light is the flow of photon particles.
2. Electrons emit from the metal surface after absorbing the energy of photons during the collisions between electrons and photons. This happens instantaneously. And one photon can emit only one electron after the collision.
3. Since one photon can emit only one electron, then each photon must have sufficient energy (equal to or greater than the work function of metal) to emit electrons. That means photons or light must have a frequency above a certain value, called threshold frequency.
4. As photons emit one electron each, then more number of incident photons will emit more electrons at a time and hence the photocurrent increases. This is why the photocurrent is directly proportional to the intensity of the incident light.
5. Now, emitted electrons can have greater energy if they absorb greater energy from incident photons. That means the energy of photons transfers to the photoelectrons. Thus, the photons or the light with greater frequency will rise the kinetic energy of the emitted photoelectrons.

## Postulates of Einstein’s theory of Photoelectric effect

Einstein said that

1. The incident light beam on the metal surface will either be absorbed completely by the metal or the entire light beam will be reflected from the metal surface.
2. If the metal absorbs the entire energy of the incident light, then some part of the energy is used to supply the work function to emit an electron from the metal surface and the rest of the energy increases the kinetic energy of the emitted electron.

## Einstein’s equation of Photoelectric effect

Let f be the frequency of incident light, W be the work function of the metal and f0 is the threshold frequency to emit electrons from metal surface.

Then, W = hf0 ………………..(1)

Now, if Emax is the maximum kinetic energy of the emitted electron then, hf = (W + Emax) ………………….(2)

Equation-2 is the Einstein equation for Photoelectric effect.

#### Other forms of Einstein equation of photoelectric effect:

Since, the work function, W=hf0 then one can write the Einstein equation as, hf = (hf0 + Emax) …………(3)

Again, if V0 is the stopping potential, then Emax = eV0

Then another form of the Einstein equation is, hf = (W + eV0) …………..(4)

## Applications of Photoelectric Effect

Photoelectric cells work on the principle of the photoelectric effect. This type of cell is used in

1. Automatic Switches
2. In Solar cell to use Solar energy.
3. Automatic Calculators
4. Automatic Camera

#### Some important questions on photoelectric effect of Einstein

1. How the photoelectric effect depends on the frequency of incident light? Answer: See the explanation by Einstein.
2. How the photoelectric effect depends on the intensity of incident light? Answer: See the explanation by Einstein.
3. What type of metals is suitable for photoelectric effect? Answer: Alkali metals like Na, K, etc. due to a low work function.

This is all from this article on Einstein’s equation and explanation of photoelectric effect by Einstein. If you still have any doubt on this topic you can ask me in the comment section.

Thank you!

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