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Einstein's Explanation Of Photoelectric Effect - A Complete Guide

Einstein's Explanation Of Photoelectric Effect - A Complete Guide

Edited By Team Careers360 | Updated on Nov 13, 2024 10:25 AM IST

Albert Einstein, one of the greatest physicists, contributed his inevitable works and proposed many theories in different fields of physics like the special theory of relativity, concepts of the black hole, photoelectric effect, Einstein quantum theory, Einstein-Maxwell equation, many more topics and some other assumptions. His instinct on the theories never fails. In any field, the Albert Einstein equation plays a prominent role and the Einstein photoelectric equation can be considered as the best achievement of his work. In 1921, he received the Nobel Prize in Physics for his work Einstein theory of photoelectric effect.

This Story also Contains
  1. What is Einstein Theory of Photoelectric Effect?
  2. Einstein Explanation of Photoelectric effect:
  3. Photoelectric Effect Derivation
  4. Numerical Problems on Photoelectric Effect
Einstein's Explanation Of Photoelectric Effect - A Complete Guide
Einstein's Explanation Of Photoelectric Effect - A Complete Guide

In this article, we will discuss about the Einstein photoelectric equation, derive the equation for the photoelectric effect. We'll also cover important related terms, such as threshold energy, work function, and stopping potential, with related solved numerical examples.

What is Einstein Theory of Photoelectric Effect?

The Einstein theory of photoelectric effect defines that- "Electrons are ejected from the surface of the metal when a ray of light incident on it." These ejected electrons are termed as Photoelectrons. The amount of electrons ejected from the from the surface will depends on the frequency of light incident on it. Let us discuss the explanation of Photoelectric effect.

Background wave

Einstein Explanation of Photoelectric effect:

Now, let us elaborate and explain the Einstein photoelectric equation as shown in the following diagram:

  • The wavy red lines represent light particles that is striking the metal surface. Energy of these photons is determined by Plank's equation:

E=hν. Where, h is Planck's constant (6.626×1034Js), ν (or f ) is the frequency of the electromagnetic wave.

  • When the light particle (photon) hits the metal surface it transfers it energy to the electrons present on the metal surface. If this energy is greater than the work function (ϕ) of the metal, then electrons overcome the attractive forces holding it in the metal.
  • The electrons will absorb the energy and leave the metal surface, as shown by the arrow directed away from the surface. These arrow represents that the electrons are leaving with Kinetic energy.
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 Photoelectric effect

In Brief we can say that the electron will leave the metal surface if the energy provided by the photons will be greater than the work function of the metal.

If the energy provided by the photons are less than the work function, no electron is released from the metal surface.

The laws of Photoelectric Emission:

  • There is a minimum cutoff frequency required for emission of electrons. Below this frequency, no electron emission occurs
  • The total number of emitted electrons increases with the intensity of incident light
  • Kinetic energy of the electrons emitted is dependent on the frequency of light and independent of intensity of light
  • There are zero time lags between the incidence of the light beam and electron emission.

Photoelectric Effect Equation

Einstein photoelectric effect equation is given by:

KEmax=hνϕ

where:

  • KEmax is the maximum kinetic energy of the ejected electrons,
  • h is Planck's constant ( 6.626×1034 J s),
  • ν (or f ) is the frequency of the incident light,
  • ϕ is the work function of the metal, which is the minimum energy needed to release an electron from the metal's surface.

Also read -

Photoelectric Effect Derivation

Let us derive Einstein’s photoelectric equation mathematically and this can be written as

Energy of photon = Energy required to remove the electron from the surface of the metal (W) + Maximum Kinetic energy of the electron which is ejected from the surface of the metal.

The energy of the incident photon ( E=hν ) is used in two parts:
- To remove the electron from the metal surface, which requires the work function W.
- To provide kinetic energy K. E. to the ejected electron.

Therefore, we can write:

hν=W+K.E


Rearranging, we get:

K.E.=hνW

At the threshold frequency ν0, the photon's energy is just enough to overcome the work function without imparting any kinetic energy to the electron. Thus:

W=hν0

3. Maximum Kinetic Energy:

Substituting W=hν0 into the kinetic energy equation, we get:

K.Emax=hνhν0

or

K.Emax=h(νν0)


For an electron with mass m and maximum velocity vmax , the kinetic energy can be expressed as:

K.Emax=12mvmax2=h(νν0)(1)

The stopping potential V0 is the potential required to bring the ejected electrons to a halt.
Thus:

eV0=12mvmax2

Substituting from equation (1), we get:

eV0=h(νν0)(2)

This equation represents the relationship between the stopping potential V0, the frequency of the incident light ν, and the threshold frequency ν0 :

eV0=h(νν0)
This final expression shows the Einstein photoelectric effect equation, showing how the maximum kinetic energy (or the stopping potential) depends on the frequency of the incident light and the material’s threshold frequency.

Scientific Terms in Photoelectric Effect

Threshold Frequency:

The minimum frequency of the given incident light beam which is required for the emission of electrons from the surface of the metal is known as Threshold frequency.

Work Function:

The minimum energy required in the removal of the electron from the surface of the metal is known as Work Function. It is represented by ϕ

Stopping potential:

The required potential to stop the emission of the electron from the surface of the metal is known as stopping potential. It is represented by V0

Numerical Problems on Photoelectric Effect


1. The threshold frequency for a certain metal is 5×1014 Hz. Calculate the work function of the metal. (Use h=6.626×1034 J ).

Solution:
1. Use the formula for the work function (ϕ) in terms of the threshold frequency (ν0) :

ϕ=hν0

where h=6.626×1034 Js and ν0=5×1014 Hz.
2. Substitute the values:

ϕ=(6.626×1034 Js)×(5×1014Hz)=3.313×1019 J

3. Convert this to electron volts ( eV ) by dividing by the charge of an electron, e=1.6×1019C :

ϕ=3.313×1019 J1.6×1019 J/eV=2.07eV
Answer: The work function of the metal is 2.07 eV .

2- Light of wavelength 400 nm is incident on a metal surface with a work function of 2.2 eV . Will electrons be ejected from the metal surface? If yes, calculate the maximum kinetic energy of the emitted electrons. (Use h=6.626×1034Js,c=3×108 m/s ).

Solution:
1. First, calculate the energy of the incident photon using E=hcλ :

E=(6.626×1034 J)×(3×108 m/s)400×109 mE=1.9878×1025 J4×107 m=4.97×1019 J

2. Convert E to electron volts:

E=4.97×1019 J1.6×1019 J/eV=3.1eV

3. Since the photon's energy ( 3.1 eV ) is greater than the work function ( 2.2 eV ), electrons will be ejected from the metal surface.
4. Calculate the maximum kinetic energy of the ejected electrons using the photoelectric equation:

KEmax=Eϕ=3.1eV2.2eV=0.9eV
Answer: Yes, electrons will be ejected, and the maximum kinetic energy of the emitted electrons is 0.9 eV .

Frequently Asked Questions (FAQs)

1. State the laws of photoelectric emission.
  • There is a minimum cutoff frequency required for emission of electrons. Below this frequency, no electron emission occurs

  • The total number of emitted electrons increases with the intensity of incident light

  • Kinetic energy of the electrons emitted is dependent on the frequency of light and independent of intensity of light

  • There are zero time lags between the incidence of the light beam and electron emission.

2. State photoelectric effect or define photoelectric emission.

The Photoelectric effect can be explained by assuming that light is incident on the surface of the metal, and then the electron in the surface of the metal gets ejected. This phenomenon of photoelectric effect was explained by the Albert Einstein Photoelectric equation.

3. Who explained the photoelectric effect initially?

The photoelectric effect was initially explained by Heinrich Hertz in the year of 1887 and later it was preceded by Lenard in the year of 1902.

4. What is the Einstein photoelectric equation? (class 12)

The Einstein photoelectric equation can be written as follows


o= ½ (mvmax2) = h (ν - νo)

5. How to calculate threshold frequency?

The threshold frequency formula can be written as W= hνo, where h is Planck’s constant and h =  6.626  x 10-34 J Hz-1

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