# Explanation of Photoelectric effect by Einstein equation

Photoelectric effect was discovered by sir Albert Einstein. There were some failures of classical mechanics to explain the photoelectric effect phenomena. Then Einstein explained the photoelectric effect on the basis of quantum theory. For this, he won the Nobel Prize in 1905. In this article, we are going to discuss the Photoelectric effect, its properties, uses and Einstein equation of photoelectric effect and explanation of photoelectric effect by Einstein. Basically, I am going to cover the chapter on photoelectric effect for class 12 students.

• 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 a 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 emission and then the motion of the electrons. This phenomena 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.

Photoelectric effect is the evidence or the proof of particle nature of light. In quantum mechanics, Max Planck said that energy of light is discrete. Then while explaining Photoelectric effect Einstein named each quantum energy of light as a Photon. So, in this process the energy of photons is converting into electrical energy. This is why this process is named as Photoelectric effect.

## 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 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 do not have enough energy to remove an electron from metal surface.

#### Stopping Potential

If a negative potential difference of anode or plate with respect to cathode is applied the photocurrent reduces. At a certain value of negative potential, the photocurrent becomes zero. The negative potential of anode with respect to 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 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 the 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. Number of emitted electrons or the photocurrent is independent of 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. Emission of electrons in Photoelectric effect is independent of the temperature of the metal surface.

## Explanation of photoelectric effect by Einsteinusing Quantum theory

Albert Einstein explained Photoelectric effect in 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 metal surface after absorbing energy of photons during the collisions between electrons and photons. This happens instantaneously. And one photon can emit only one electron after collision.
3. Since one photon can emit only one electron, then each photon must have a sufficient energy (equal to or greater than the work function of metal) to emit electrons. That means photons or the light must have the 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 transfer into 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 entire light beam will be reflected from the metal surface.
2. If the metal absorbs 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 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 electron from metal surface.

Then, W = hf0 ………………..(1)

Now, if Emax be 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 be the stopping potential, then Emax = eV0

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

## Applications of Photoelectric Effect

Photoelectric cells work on the principle of photoelectric effect. Now, this type of cells have uses in

1. Automatic Switches
2. Solar cell
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 are suitable for photoelectric effect? Answer: Alkali metals like Na, K, etc. due to low work function.

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

Thank you!

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