# Work Function: Definition, Concept, and Formula

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What is work function? Work function definition: as the minimum amount of energy required by an electron to escape from a metal surface. Or work function definition: Is the minimum quantity of energy that is required to remove an electron to infinity from the surface of a given solid, usually a metal.

Work function is also defined as the energy that is needed for a particle to come from the interior of a medium and break through the surface used especially of the photoelectric and thermionic emission of electrons from metals

# Work Function: Definition, Concept, and Formula

Work function can be explained and defined by Classical Physics and Quantum Physics. Here we will discuss concept of work function in Classical Physics and Quantum Physics. Let’s see below.

## Concept of Work Function in Classical Physics

The concept of work function is not to hard to understand. Either classical physics or quantum mechanics can explain the concept. According to established material science, when an electron attempts to escape from a metal surface, it deserts a positive picture in the metal surface.

Due to the attraction of this positive picture, the negative electron swings back to metal surface subsequently can’t leave the the metal crystal permanently. In any case, to conquer this fascination drive an electron requires adequate energy supplied from outside usually from external light sources.

The minimum energy required just to escape an electron from a metal surface is known as work function.

## Concept of Work Function in Quantum Physics

Work function can also be explained and defined by quantum physics. For that, we first must know some basic features.

1. Sir Albert Einstein said that light is as a light emission colossal number of discrete energy packets called photons. The energy contained in every photon is hf. Where h is Planck Constant and f is the frequency of light.
2. Now when the light strikes on a metal surface electrons on the surface of the metal get energy from the light and get emitted from the surface. This phenomenon is classically termed as photoemission.
3. As the energy of one photon Ephoton = hf, the energy of each photon depends upon the frequency of light. Hence, the frequency is only variable upon which energy of photon rather light depends., It is found that there is no photoemission from a metal surface below a certain frequency of light. Hence, for photoemission minimum frequency of incident light is required.
4. If the frequency of light is higher than that previously mentioned least frequency, the additional energy of photon will be changed over to kinetic energy of the emitted electron. Hence, how quick the electron will be discharged from the outside of the metal relies on the frequency of occurrence light. Not on the intensity (Brightness of the light).
5. But when an intensity of incident light gets expanded without changing its frequency. Obviously, the number of photons strike on the metal surface increases hence more emitted electrons will be produced, but the kinetic energy of each electron will be unchanged as the frequency of incident light is fixed, in that case.
6. Threshold Frequency: Hence after a certain minimum frequency of incident light, the electrons start emitted from a metal surface. Over this frequency, the kinetic energy of the emitted electron is directly proportional to incident light frequency. But below this minimum frequency, there will be no kinetic energy in the electrons. This is called threshold frequency.
7. The frequency of incident light below which no photoemission on a metal surface gets started is called threshold frequency for that metal. The value of threshold frequency is different for different metals.

## Work Function Formula

The gain of kinetic energy of an electron is the difference between incident photon energy and work function of the metal or material and that can be represented as:

Where:

• φ is the work function of the metal and
• Ek is the kinetic energy gain of the electron.

The equaltion can be rewritten as:

Where:

• fo is threshold frequency of the metal.