Physics
Study Material

# Stopping Potential in Photoelectric Effect

The stopping potential is also known as cut off potential. It is the negative potential at which the photoelectric current becomes zero.

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Posted by Mahak Jain, 24/11/2021

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The phenomenon of photoelectric emission was discovered in 1887 by Heinrich Hertz. Later Heinrich Rudolf Hertz experimentally proved the photoelectric effect. We define the photoelectric effect as follows: When a light radiation of suitable frequency was incident on a metal surface by a suitable light source. It facilitates the escape of free, charged particles known as electrons. The stopping potential is also known as cut off potential. It is the negative potential at which the photoelectric current becomes zero.

## What is the photoelectric effect ?

The photoelectric effect is emission of electrons when electromagnetic radiation hits a material. The emitted electrons in this manner are called photoelectrons.

The process by which photoelectrons emits from the surface of the metal due to the action of light is photoemission.

The photoelectric effect occurs when the electrons at the surface of metal absorb energy. These electrons use energy to overcome their attractive force with metal nuclei which tends to bind them to metal surface.

The emitted photoelectrons and their kinetic energy depends of frequency of electromagnetic radiation which hits metal surfaces,

Thus, KE = h ( v – v0 )

Here h = plank constant

v = frequency of incident light

v0 = the threshold frequency for the metal

## Stopping potential definition

The stopping potential is also known as cut off potential. It is the negative potential at which the photoelectric current becomes zero.

It is the potential required to stop the removal of electrons from metal surface when the incident light energy is greater than the work potential of the metal on which the incident light is directed.

The stopping voltage in electron volt is equal to the maximum kinetic energy of the electron,

KEmax = eV0

The stopping potential or cut off potential does not depend on the intensity of incident radiation. On increasing the intensity, it remains unchanged. On increasing intensity, the value of saturated current increases.

The cut off potential depends on the frequency. The stopping potential or cutoff potential is directly proportional to the frequency. Higher the frequency of incident light higher the value of stopping potential.

## Stopping potential formula

It is the potential required to stop the removal of an electron from a metal surface when the incident light energy is greater than the work potential of the metal on which the incident light is directed. I is represented by V0.

KEmax = hv – φ0 (for v > v0)

eV0 = hv – φ

Thus, V0 = (h/e)v – φ/e

φ0 : work function

## What is stopping potential ?

The stopping potential refers to the voltage differences that is required to stop the electrons from moving across the metal plates in photoelectric effect.

Light is directed at  the metal plate C. The frequency of light v is high enough, electrones will be ejected from the plate and will travel across to plate A.

If we add a voltage source to the circuit so that it creates a negative charge on plate A and a positive charge on plate C. The electron ejected from C will be repelled by the negative electrode.

Now we increase the voltage, we will increase the electric repulsion forces between ejected electrons and negative electrodes. Gradually a point reached when no electrons have sufficient kinetic energy to move across to reach plate A. This is called the stopping voltage (V0) of stopping potential.

eV0 = hv – φ

Here V0 is the stopping voltage.

## Effect of frequency of incident radiation on stopping potential

The stopping potential or cutoff potential is more negative for higher frequencies of incident radiation.

If the frequencies are in the order ν3 > ν2 > ν1 then the stopping potentials are in the order V03 > V02 > V01

For a given photosensitive material

• if frequency of incident radiation is above the threshold frequency,  the photoelectric current is directly proportional to the intensity of incident light
• the stopping potential does not depend on its intensity of radiation.
• saturation current is directly proportional to the intensity of incident radiation.

## Stopping potential vs frequency graph

For a given photosensitive material, the stopping potential V0 varies linearly with the frequency of incident radiation.

There is a certain minimum cut-off frequency ν0 for which the stopping potential is zero. The incident radiation after overcoming this minimum frequency v0, the stopping potential increases linearly with frequency of stopping radiation.