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Einstein's Photoelectric Equation - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

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  • 83 Questions around this concept.

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When photons of wavelength λ1 are incident on an isolated sphere, the corresponding stopping potential is found to be V.  When photons of wavelength  λ2 are used, the corresponding stopping potential is thrice that of the above value. If light of wavelength  λ3 is used then find the stopping potential for this case :

Question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.

Statement-1: When ultraviolet light is incident on a photocell, its stopping potential is V_{0} and the maximum kinetic energy of the photoelectrons is K_{max}. When the ultraviolet light is replaced by X-rays, both V_{0} and K_{max} increase.

Statement-2:  Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.

 

This question has Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements :

Statement 1: A metallic surface is irradiated by a monochromatic light of frequency \upsilon > \upsilon _{0} (the threshold frequency). The maximum kinetic energy and the stopping potential are K_{max}\; and V_{0} respectively. If the frequency incident on the surface is doubled, both the K_{max}\; and V_{0}  are also doubled.

Statement 2: The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light.

 

Two identical photo cathodes receive light of frequencies f_{1}\, and\, f_{2}. If the velocities of the photoelectrons (of mass m ) coming out are respectively v_{1}\, and\, v_{2} , then

According to Einstein’s photoelectric equation, the plot of the kinetic energy of the emitted photoelectrons from a metal and the frequency of the incident radiation gives a straight line whose slope is:

Concepts Covered - 1

Einstein's Photoelectric equation

Einstein's Photoelectric equation-

 

                                                                                    

As we studied that E = hν  is the equation of energy of each photon. Now we have also studied that the threshold frequency is that frequency below which the electrons won’t come out of the metallic surface. From the above equation we see that Energy is a function of frequency. Now one question will come in mind that when the electron gets ejected then where does all the electron goes?? Does that electron have some energy to go any where??? If yes then which type of energy??

All these type of question was well answered by the greta scientist Albert Einstein, According to the experiment performed by the Albert Einstein, there are some conclusion that those electron have kinetic energy only. Also the energy absorbed by the photons is partly used to overcome the force by the metallic surface. SInce there is no electric field present outside the metallic surface so there will be only energy present is pure kinetic energy. 

So, we have K.E. of the photo-electrons = (Energy obtained from the Photon) – (The energy used to escape the metallic surface)

Here, The energy used to escape the metallic surface is the wrok function (\phi) which we have discussed already. So the Einstein’s Photoelectric equation can also be written as - 

                                                                                                                      \mathrm{K.E.}=\mathrm{hv}-\Phi

We can understand the work function more clearly like this - 

As we know that an electron needs some minimum energy to be extracted from a metallic surface. So from the above equation, if ν = threshold frequency (ν0) then the electrons gets just enough quantum energy to come out of the metal. It means that the Kinetic Energy of such an electron will be zero. So we can write that - 

                                                                                                        \mathrm{hv}_{0}-\Phi=0 \text { or } \mathrm{hv}_{0}=\Phi

This is the relation between the threshold frequency and the work function. We can also change this equation in terms of the threshold wavelength. 

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Einstein's Photoelectric equation

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