How Does Electron Work Function Impact the Photoelectric Effect?
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.
So,
E = hf (as we know already)
E = hf = + EK = hf0 = 1/2mv2
Here,
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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Here,
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 Explained with Examples
1. What is the electron work function of a metal?
The electron work function (often denoted by the symbol Φ or W) is the minimum amount of energy required to remove a free electron from the surface of a metal. Think of it as an 'exit fee' that an electron must pay to escape the attractive forces holding it within the material. This value is a characteristic property of the metal itself.
2. What are the common units and symbol for work function?
The work function is most commonly measured in electron-volts (eV). It can also be expressed in Joules (J), but eV is more convenient for the atomic scale. The standard symbol for work function is the Greek letter Phi (Φ), although 'W' is also sometimes used.
3. How is the work function related to threshold frequency and wavelength?
The work function defines the minimum energy needed for photoemission, which corresponds to a minimum frequency (threshold frequency, ν₀) and a maximum wavelength (threshold wavelength, λ₀) of incident light. The relationship is given by the formulas:
- Φ = hν₀
- Φ = hc/λ₀
4. Why does the work function differ for different metals?
The work function varies between metals because it depends on how strongly each metal holds onto its electrons. This is influenced by several factors at the atomic level, including:
- The positive charge of the nucleus.
- The arrangement of electrons in their shells.
- The density and structure of the crystal lattice.
5. What is the practical significance of a material's work function?
The work function is a critical parameter in designing and selecting materials for various electronic devices that rely on electron emission. For instance:
- Photocells and Photomultipliers: Materials with a low work function are chosen for cathodes to ensure they are highly sensitive to light and can easily emit electrons.
- Solar Cells: Understanding the work functions of different layers in a solar cell is crucial for efficient separation of charge and generation of electric current.
- Vacuum Tubes: The cathodes in vacuum tubes are coated with materials having a low work function to allow for efficient thermionic emission (emission of electrons due to heat).
6. How is work function different from ionisation energy?
While both concepts involve removing an electron, they apply in different contexts. Work function is the minimum energy to remove an electron from the surface of a solid material (a crystal lattice). In contrast, ionisation energy is the energy required to remove an electron from a single, isolated atom in its gaseous state. The work function is generally lower than the ionisation energy for the same element due to the interactions within the metallic crystal structure.
7. How does the work function explain the existence of a threshold frequency in the photoelectric effect?
The work function acts as a fundamental energy barrier. According to Einstein's photoelectric equation, the energy from an incident photon (E = hν) is used for two things: overcoming the work function (Φ) and providing kinetic energy (K.E.) to the emitted electron. So, hν = Φ + K.E. For an electron to be emitted, it must at least overcome the barrier, meaning the photon's energy must be at least equal to the work function (hν ≥ Φ). This minimum energy requirement directly translates to a minimum frequency, known as the threshold frequency (ν₀), below which no emission can occur, regardless of the light's intensity.
8. Can the work function of a metal be changed?
Yes, while the work function is an intrinsic property of a pure, ideal metal, its effective value can be influenced by several external and surface factors. These include:
- Surface Purity: Even a thin layer of impurities or oxidation on the surface can significantly alter the work function.
- Temperature: The work function can show a slight dependence on temperature.
- Crystal Face: For a single crystal, different crystallographic faces can exhibit slightly different work functions.
- External Electric Field: Applying a strong external electric field can lower the effective work function, a phenomenon known as the Schottky effect.
