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Electron Work Function

Last updated date: 09th Apr 2024
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Work Function of an Electron

When a metal like Cesium is provided energy, electrons start emitting from its surface. So, the more tightly the electrons are held, the more will be the energy required to release electrons.

A parameter that measures the magnitude of energy to remove the electron, as and when required is the electron work function. The electronic work function is akin to work, so it is measured in Joules.

The minimum energy required to release electrons is the photoelectric effect work function.

On this page, we will discuss in-depth the work function of an electron with the working of the photoelectric effect.

Electronic Work Function

The idea of a work capacity can be clarified in both traditional physical science or quantum mechanics. According to old-style physical science, when an electron attempts to escape from a metal surface, it gives up a positive picture in the metal surface. 

Because of the fascination of this positive picture, the negative electron turns around to the metal surface thus can't leave the metal precious stone forever. However, to beat this fascination power an electron requires adequate energy provided from outside as a rule from outer light sources. The base energy required just to expel an electron from a metal surface is known as electronic work function.       


Photoelectric Effect Work Function

Do you know why we consider the Photoelectric effect in the photoelectric work function?

Well! The energy we provide to the metallic surface is in the form of packets called photons. So,  electrons emitting from the surface under the effect of energy (photon-energy) are photoelectrons.

For understanding how electrons come out of the surface and if there is any effect on the kinetic energy and work function of electrons, we study the photoelectric work function.

The work function is the attainable energy needed to detach electrons from the metal surface. So, the maximum energy EK of the photoelectron will be equal to the energy of the incident photon (hf) minus the work function (), because an electron has to do some work to escape the potential from the metallic surface.

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The equation for the above statement is given as;

EK = hf - …..(1)

In other words, the photoelectron outside of the metallic surface will not have the same energy as that of the incident photon because some of its energy is utilized coming out of the surface. 

The above equation (1) says the same thing that’s why the work function is deducted from the exact energy equation “E = hf”, as the Planck relation or the Planck-Einstein equation.

Planck-Einstein Equation

The Planck-Einstein equation is given as;

                 E = hf (work function energy)

Sir Albert Einstein said that light is a light emission of a gigantic number of discrete energy bundles called photons. The energy contained in every photon is hf. Where h is Planck Constant and f is the recurrence of light.

Photoelectric Effect

In the above text, we understand that work function is the amount of minimum effort required to free electrons from the lattice of a metal. Also, we learned that under the effect of photoelectric work function, electrons utilize some of their energy coming out of the tightly-held lattice points.

Now, let’s understand the concept of kinetic energy and work function:

Firstly, what happens is, all the energy from the photon is absorbed by electrons, which is then utilized by electrons to free from the surface and perform the work. The remaining energy is converted into kinetic energy ( EK) of the photoelectron.


                 E = hf  (as we know already) 

                 E = hf = +   EK = hf0 = 1/2mv2


f0 = threshold frequency. It is the frequency of the quantum of the minimum energy required to free electrons, measured per second.

Point to Note:

No emission takes place if the photon energy is less than the work function; this statement can be expressed as;

               E > (has to be greater than)

If not, then the emission of electrons will not take place.

So, from the above context, we understood the working of photoelectric effect.

Work Function Energy

Below is the work function graphical representation :

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The vertical axis (y-axis) depicts the energy of an electron, and the horizontal axis (x-axis) represents the frequency.

From the above graph, we notice that after the threshold frequency, “f0” Hz, the kinetic energy of electrons starts increasing proportionally with frequency.

Photoelectric Function and Work Function

In the event that E < Φ, no photoelectric effect will occur. 

In the event that E = Φ, simply photoelectric effect will occur however the dynamic energy of launched out photoelectron will be zero 

In the event that E > photoelectron will be zero 

In the event that E > Φ, the photoelectric effect will happen alongside ownership of the dynamic energy by the catapulted electron.

Do You Know?

The photoelectric impact was found in 1887 by a German physicist named Heinrich Rudolf Hertz. 

Regarding work on radio waves, Hertz saw that, when bright light gleams on two metal terminals with a voltage applied across them, the light changes the voltage at which sparkling happens.

FAQs on Electron Work Function

1. What is Photoelectron Emission?

Ans: At the point when packets of energy called the photon strikes on a metal surface electrons on the outside of the metal get energy from the light and get transmitted from the surface. This wonder is traditionally named photoemission. 

As the energy of one photon Ephoton = hf, the energy of every photon relies on the recurrence of light. Thus, the recurrence is just a factor whereupon energy of photon rather light depends., It is discovered that there is no photoemission from a metal surface under a specific recurrence of light. Henceforth, for photoemission least frequency of episode light is required.

2. How Does Frequency Affect the Photoelectric Effect?

Ans: For the photoelectric effect to happen, the photons that are occurring on the outside of the metal should convey adequate energy to defeat the appealing powers that tight spot the electrons to the cores of the metals. 

The fundamental measure of energy needed to eliminate an electron from the metallic surface is known as the threshold energy (signified by the symbol Φ). For a photon to have energy equivalent to the threshold energy, its frequency should be equivalent to the limit recurrence (which is the threshold frequency of light needed for the photoelectric impact to happen). 

The threshold frequency is generally meant by the image fth and the related frequency (called the threshold wavelength) is indicated by the image λth. The connection between the threshold energy and the threshold frequency is communicated as follows. 

                               Φ = h fth = hc/λth

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