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Question
Define the terms (i) ‘cut-off voltage’ and (ii) ‘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.
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Solution
When light of sufficiently small wavelength is incident on a metal surface, electrons are ejected from the metal. This Phenomenon is called the photoelectric effect.
(i) The cathode is illuminated with light of some fixed frequency v and fixed Intensity I1. A small photoelectric current is observed due to few electrons that reach anode just because they have sufficiently large velocity of emission. If we made the potential of the anode negative with respect to cathode then the electrons emitted by cathode are repelled. Some electrons even go back to the cathode so that the current decreases. At a certain value of this negative potential, the current is completely stopped. The least value of this anode potential which just stops the photocurrent is called cut off potential or stopping potential.
(ii) For a given material, there is a certain minimum frequency that if the incident radiation has a frequency below this threshold, no photoelectric emission will take place, howsoever intense the radiation may be falling.
(iii) According to Einstein’s photoelectric equation, maximum K. E is given as
`K.E_(max) =(hc)/lambda phi = hv -phi`
Where λ is wavelength and ν is corresponding frequency and Φ is work function.
We expose a material to lights of various frequencies and thus photoelectric current is observed and cut off potential needed to reduce this current to Zero is noted. A graph is plotted and that is straight line.
At ν0 the stopping potential is zero this means at this frequency the incident light is not able to eject electrons this is threshold frequency. Extended this line gives the cut off potential to make the photo
current zero which is `(-phi)/e`
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A student performs an experiment on photoelectric effect, using two materials A and B. A plot of Vstop vs ν is given in Figure.
- Which material A or B has a higher work function?
- Given the electric charge of an electron = 1.6 × 10–19 C, find the value of h obtained from the experiment for both A and B.
Comment on whether it is consistent with Einstein’s theory:
