question_answer

Write Einstein's photoelectric equation. State clearly how this equation is obtained using the photon picture of electromagnetic radiation. Write the three salient features observed in photoelectric effect which can be explained using this equation.    Or What is photo-electric effect? Write Einstein's photoelectric equation. Explain how it enables us to understand the (i) linear dependence, of the maximum kinetic energy of the emitted electrons, on the frequency of the incident radiation. (ii) existence of a threshold frequency for a given photoemitter. (iii) independence of the maximum energy of emitted photo-electrons from the intensity of incident light.                            

Answer:

                Photo-electric effect is the phenomenon of emission of electrons from the surface of metals, when light radiations of suitable frequency fall on them. Einstein photo-electric equation is in accordance with the energy conservation law as applied to the photo-absorption by an electron in the metal. Thus Energy of incident photon \[=\]Maximum K.E. of photoelectron \[+\]Work function of metal or       \[hv=\frac{1}{2}m\upsilon _{\max .}^{2}+{{W}_{0}}\] or            \[{{K}_{\max }}=\frac{1}{2}m\upsilon _{\max .}^{2}=hv-{{W}_{0}}\] At threshold frequency \[{{v}_{0}}\] , no K.E. is given to the electron. So \[h{{v}_{0}}={{W}_{0}}\] Hence   \[{{K}_{\max }}=hv-{{W}_{0}}=h(v-{{v}_{0}})\] This is Einstein's photoelectric equation. (i) Clearly, above the threshold frequency \[{{v}_{0}},{{K}_{\max }}\propto v\]i.e., the maximum K.E. of the emitted electrons depends linearly on the frequency of incident radiation. (ii) When \[v<{{v}_{0}},{{K}_{\max }}\]becomes negative. The kinetic energy becomes negative which has no physical meaning. Hence there is no photo-electric emission below the threshold frequency \[{{v}_{0}}\] . (iii) It is obvious from the photo-electric equation that the maximum K.E. of photo-electrons does not depend on the intensity of incident light.