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# Photoelectric Effect

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 Sub Topics The photoelectric effect is the most important interaction of low-energy photons with matter. In this effect a photon of energy h$\nu$ is absorbed by an atom and an electron of particular energy is ejected. This effect arises when a solid body is illuminated with light. If the light has a sufficient high frequency, then electrons are emitted from the body. This was the first peculiar fact about the photoelectric effect.The photoelectric effect was discovered by Heinrich Hertz and extensively studied by Hallwachs, Lenard and Millikan.  It is identical to the thermionic emission of electrons. In photoelectric emission, the electrons in the metal escape from the metal surface using energy from the incident radiation whereas in thermionic emission, energy in the form of heat is absorbed by the electrons.

## Definition

The phenomenon of emission of electrons from a metallic surface when illuminated by light of suitable frequency is called the photoelectric effect.

Characteristics of photoelectric effect are:

• The photoelectric current increases with increase of intensity of incident light, but is independent of frequency on incident light.
• The maximum kinetic energy of emitted electrons increases with increase of frequency and is independent of incident light.
• There is no time lag between incident of light and emission of electrons.
Important terms related to the photoelectric effect are,

Threshold frequency: The minimum frequency of incident light which can eject photo electrons from a metallic surface .

Threshold wavelength: The maximum wavelength of incident light which can eject photo electrons from a metallic surface.

Stopping potential: The minimum negative potential applied to anode which stops the photoelectric current

Photon: A photon is a quantum of light energy(electromagnetic energy).

## Equation

According to Einstein, the photoelectric effect equation is,

E = W + K.Emax.................(1)

We know that,

E = h$\nu$

W is the work function and it is given as, h$\nu_{0}$

K.Emax = $\frac{1}{2}mv_{max}$ = e$V_{0}$

Substitute these equations in (1)

h$\nu$ = h$\nu_{0}$ + $\frac{1}{2}mv_{max}$

h$\nu$ - h$\nu_{0}$ = e$V_{0}$

h($\nu$ - $\nu_{0}$) = e$V_{0}$

Put $\nu$ = $\frac{c}{\lambda}$

So, hc($\frac{1}{\lambda}$ - $\frac{1}{\lambda_{0}}$) = e$V_{0}$....................(2)

where h is the Planck's constant, c is the velocity of light, $\lambda$ is the wavelength of the incident light, $\lambda_{0}$ is the threshold wavelength, e is the charge of the electron and $V_{0}$ is the stopping potential.

Equation(2) represents the equation of photoelectric effect.

## Experiment

As mentioned before, photoelectric effect is formulated by Hertz and it is scientifically proved by Millikan and Thomson. From this experimental results, Einstein gave a mathematical explanation and it is considered as the photoelectric effect equation. During this process, when a light beam is incident on a metal surface, an electron ejected from the surface. So, here light energy is converted as the electrical energy.

Experiment:

The experimental set up is consists of an evacuated quartz tube, photosensitive plates emitter (P) and collector (C). P is connected to the negative terminal of the electric supply and C is connected to the positive terminal. The potential difference between these two place can be adjusted by using a rheostat.

When light beam of sufficient intensity is incident on P, the photo-electrons are emitted and collected in plate C. Due to this, photo current will flow through the circuit and can be measured using galvanometer.

The graphical representation of photoelectric effect is given below:

The graph is drawn between stopping potential and frequency. The frequency at which the photo current starts is known as the threshold frequency.

## Work Function

Work function is defined as the minimum amount of energy required to release an electron from the surface of metal or from its atomic binding. It is denoted by $\Phi$.

The mathematical representation of the work function is given as,

$\Phi$ = h$\nu_{0}$
Where $\Phi$ is the work function
h is the Planck's constant (6.626$\times10^{-34}$ Js)
$\nu_{0}$ is the threshold frequency

## Applications

Some of the applications of photoelectric effect is listed below:

1. This principle is used in the photoelectric cell
2. For reproducing the sound in cinematography, this principle is used
3. Automatic switching system in street lights
4. Television transmission
5. Used in traffic signals
6. Burglar alarm is another application of photoelectric effect

## Photoelectric Effect Problems

Let us discuss the problems of photoelectric effect in this section.

### Solved Examples

Question 1: The work function of polished silver is 4.73eV. Calculate the wavelength of the beam that can eject a photo-electron?

Solution:

Given that,
The work function of polished silver, $\Phi$ = 4.73eV
Equation for work function is,
$\Phi$ = h$\nu_{0}$

= $\frac{hc}{\lambda_{0}}$

$\lambda_{0}$ = $\frac{hc}{\Phi}$

= $\frac{6.626\times10^{-34}\times3\times10^{8}}{4.73}$

= $0.3970\times10^{-26}$ m

Question 2: Calculate the work function of a metal, if the threshold wavelength is 263nm?

Solution:

Given parameters are,
$\lambda_{0}$ = 263 nm = 263$\times10^{-9}$ m
Equation for work function is,

$\Phi$ = h$\nu_{0}$ = $\frac{hc}{\lambda_{0}}$

So, $\Phi$ = $\frac{6.626\times10^{-34}\times3\times10^{8}}{263\times10^{-9}}$ = 7.5$\times10^{-19}$ eV