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Einstein's Photoelectric Equation – When the light falls on the surface of the metal, the electrons emits from its surface, this phenomenon is called Photoelectric Effect. Using this idea, Albert Einstein shows a new image of photoelectric emission and has given an equation, known as Einstein’s Photoelectric Equation. This article will help you understand the Einstein’s explaination of Photoelectric emission.
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Key Terms: Photoelectric Effect, Einstein Photoelectric Equation, Photoelectric Emission, Photons, Light, Electrons
Photoelectric Effect
Photoelectric Effect is a phenomenon in which the metal surface, when struck with the light of sufficient frequency, it emits electrons. The phenomenon was first documented by Heinrich Hertz in 1887, and then in 1902 by Lenard, but there were few anomalies as Maxwell’s electromagnetic wave theory of light could not explain the photoelectric effect. Einstein used the idea of Planck that light is a particle and resolved the problem that existed with the Photoelectric effect beforehand. Einstein showed that each particle of light, known as photon or quanta, carries energy in the form of packets that depends on the frequency of light, denoted by
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Features of Photoelectric Effect
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- Above the value of a certain frequency, known as the threshold frequency, the photoelectric current’s strength depends on the light radiation’s intensity.
- Any value of frequency that is below the threshold frequency is unable to generate the photoelectric current.
- The stopping potential is known as the reverse potential that is at play when the photo-current stops. Hence, the source of light, no matter how intense, can defeat the stopping voltage.
- As soon as the source of the light is turned on, the electron is popped out. That means the photoelectric effect is instantaneous.
Einstein’s Photoelectric Equation
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The equation for the photoelectric effect is
E = hv
Where,
- E is the energy
- h is Planck’s constant which is equal to 6.6261 × 10-34 Js.
- And is light’s frequency
Einstein postulated that light is packed up into photons and when these photon falls onto the metal’s surface, the entire energy of the photon is transferred to the electron. Some of this transferred energy is used in order to remove the electron from the grasp of the atom of the metal. During this collision, the electrons that are emitted from underneath the surface of the metal lose some amount of kinetic energy but the electrons that are present on the surface have the maximum amount of kinetic energy as they carry with them the kinetic energy that is emitted by the photons. This can be mathematically represented as
E = W + KE
Where E is the energy of photon
W is the work function, which represents the energy that is required to eject an electron
And KE is the maximum kinetic energy of the electron
Hence, we can say that
hv = W + KE
KE = hv – W
At the threshold frequency, the amount of electrons that are ejected are ν0 and they don’t possess any kinetic energy. Under this threshold frequency, no electron emission takes place. Hence, the work function of the metal, denoted by W, must be the energy of a photon with this frequency.
Therefore, W = hv0
So, the equation for maximum amount of kinetic energy is
KE = 1/2mv2max = hv– W
1/2mv2max = h(v−v0) (since, W = hv0)
where the maximum kinetic energy of the electron is denoted by Vmax. The maximum kinetic energy is experimentally calculated by using the stopping potential.
Stopping Potential = ev0 =1/2mv2max = h(v−v0)
Thus, the value of h obtained fron the above eguation led to the acceptance of Einstien’s explaination of Photoelectric effect.
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Things to Remember
- When the light falls on the surface of the metal, the electrons emits from its surface, this phenomenon is called Photoelectric Effect.
- Photoelectric Effect is a phenomenon in which the metal surface, when struck with the light of sufficient frequency, it emits electrons.
- Einstein used the idea of Planck that light is a particle and resolved the problem that existed with the Photoelectric effect beforehand.
- The stopping potential is known as the reverse potential that is at play when the photo-current stops.
- Hence, the source of light, no matter how intense, can defeat the stopping voltage.
-
The equation for the photoelectric effect is E = hv.
Previous Year Questions
- In the ideal double-slit experiment, when a glass-plate….[JEE Advance 2002]
- An example for the best source of monochromatic light is… [JKCET 2019]
- When the light of frequency 2v0 is incident on a metal plate….[NEET 2018]
- When the source is moved to a distance of 1.0m , the number of photo electrons liberated will….[NEET 2007]
- An electron of mass m with an initial velocity enters...[NEET 2018]
Sample Questions
Ques. The stopping potential in an experiment on photoelectric effect is 1.5 V. What is the maximum kinetic energy of the photoelectrons emitted? (2 Marks)
Ans. At stopping potential, no electron reaches the plate. It means that the energy of electrons is compensated by energy equivalent to stopping potential.
KEmax =ev0
Where,v0 = cut-off potential
KEmax = 1.5 eV
Ques. Write three basic properties of photons which are used to obtain Einstein’s photoelectric equation. Use this equation to draw a plot of maximum kinetic energy of the electrons emitted versus frequency of incident radiation. (3 Marks)
Ans. The three basic properties of photons are:
(i) Photons are the carriers of energy.
(ii) Energy of a photon is directly proportional to the frequency of light.
(iii) The photon transmits all its energy to the electron with which it comes in contact.
Einstein’s photoelectric equation
1/2mv2max = hv– W
The graph is shown below:
Ques. Write Einstein’s photoelectric equation. State clearly the three salient features observed in photoelectric effect which can be explained on the basis of above equation. (3 Marks)
Ans. Einstein's photoelectric equation for a single photon ejecting is
Kmax = hv -W
Where E = energy of photon
W = work function, which represents the energy that is required to eject an electron
And Kmax = maximum kinetic energy of the electron
At the threshold frequency, the amount of electrons that are ejected are ν0 and they don’t possess any kinetic energy. Under this threshold frequency, no electron emission takes place. Hence, the work function of the metal, denoted by W, must be the energy of a photon with this frequency.
Therefore, W = hv0
So, the equation for maximum amount of kinetic energy is
Kmax = hv– hv0
Kmax = h(v−v0)
The equation is obtained by considering the particle nature of electromagnetic radiation.
Three Salient features observed on the basis of Einstein's Photoelectric Effect are-
- When the frequency of an incident photon increases, the kinetic energy of an emitted electron increases.
- When intensity of incident light increases, the number of incident photons increases, as one photon ejects one electron. It also means that the photocurrent will increase with increase of intensity.
- When the energy of the incident photon is greater than the work function, the photoelectron is ejected with an immediate effect. So, there is no time lag between incidence of light and emission of photoelectrons.
Ques. Write Einstein’s photoelectric equation and point out any two characteristic properties of photons on which this equation is based. Briefly explain three observed features which can be explained by this equation. (3 Marks)
Ans. The characteristics of photons are:
(i) Energy of photons is directly proportional to the frequency
(ii)Energy of photons is inversely proportional to the wavelength
(iii) In photon-electron collision, total energy and momentum of the system of two constituents remains constant.
Features of photoelectric effects
(i) Explanation of frequency law: When frequency of incident photon (n), increases, the kinetic energy of emitted electrons increases.
(ii) Explanation of intensity law: When intensity of incident light increases, the number of incident photons increases, as one photon ejects one electron. Photocurrent will increase with increase of intensity. Frequency has no effect on photocurrent.
(iii) Explanation of the no time lag law: When the energy of the incident photon is greater than the work function, the photoelectron is immediately ejected. That is why there is no time lag between incidence of light and emission of photoelectrons.
Ques. (i) State three important properties of photons which describe the particle picture of electromagnetic radiation.
(ii) Use Einstein’s photoelectric equation to define the terms:Stopping potential and Threshold frequency. (3 Marks)
Ans. Three important properties of photon are -
(a) Photons are massless, have no electric charge and are stable.
(b) Photons can be emitted in many natural processes.
(c) The photon carries spin angular momentum that does not depend on its frequency.
(ii) Einstein's photoelectric equation is given by
Kmax =h (v – v0)
- Stopping potential is the minimum negative potential given to a plate with respect to the cathode, at which no photoelectron reaches the plate. It is represented by V0.
- The minimum frequency of the incident radiation below which no emission of photoelectrons takes place is called the threshold frequency.
Ques. Define the terms cut-off voltage and threshold frequency in relation to the phenomenon of photoelectric effect. Using Einstein’s photoelectric equation shows how the cut-off voltage and threshold frequency for a given photosensitive material can be determined with the help of a suitable plot/graph. (3 Marks)
Ans. Cut- off Voltage- The minimum negative anode voltage at which the photo-current of the circuit reduces to zero is called the Cut-off Voltage (v0 ).
Threshold Frequency- The minimum frequency below which photo-electrons do not get emitted is called threshold frequency (V0).
Einstein's equation is
Kmax =h v – h v0
so, eV0 = h v – h v0
or V0=eh (v – v0)
Now the variation of stopping potential or cut-off potential (v0 ) with incident frequency (V) is shown in figure.
We can calculate the threshold frequency from the point of intersection on the frequency axis and cut-off voltage from the point of intersection on the potential axis.
Ques. What is the equation of the photoelectric effect? (2 Marks)
Ans. The equation for the photoelectric effect is
E = hν
Where, E = energy
h= Planck’s constant which is equal to 6.6261 × 10-34 Js.
And = light’s frequency
Ques. What is the threshold frequency? (1 Mark)
Ans. Above the value of a certain frequency the photoelectric current’s strength depends on the light radiation’s intensity. This certain frequency is called the threshold frequency.
Ques. What is known as photoelectric effect? (2 Marks)
Ans. The phenomenon in which the metal surface, when struck with the light of sufficient frequency, emits electrons, is known as the photoelectric effect. Einstein, using the revolutionary idea of Planck - the particle nature of the light explained the phenomenon of photoelectric effect.
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