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Obtain Einstein's photoelectric equation with necessary explanation. |
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Answer» Solution :When a photon of energy HV is incident on a metal surface, it is completely absorbed by a single electron and the electron is ejected. In this process, a part of the photon energy is used for the EJECTION of the electrons from the metal surface (PHOTOELECTRIC work function `phi_(0)`) and the remaining energy as the kinetic energy of the ejected electron. From the law of conservation of energy. `h upsilon = phi_(0) + (1)/(2) mv^(2)""...(1)` where m is the mass of the electron and `upsilon` its velocity  If we reduce the frequency of the incident light, the speed or kinetic energy of photo electrons is also reduced. At some frequency `v_(0)` of incident radiation, the photo electrons are ejected with almost zero kinetic energy. Then the equation (1) becomes `h upsilon_(0) = phi_(0)` where `v_(0)` is the THRESHOLD frequency. By rewriting the equation (1), we get `h upsilon = h upsilon_(0) + (1)/(2) mv^(2)""...(2)` The equation (2) is known as Einstein.s Photoelectric equation. If the electron does not lose energy by internal collisions, then it is emitted with maximum kinetic energy `K_(max)`. Then `K_(max) = (1)/(2) mv_(max)^(2)` where `upsilon_(max)` is the maximum velocity of the electron ejected. The equation (1) is rearranged as follows : `K_(max) = h upsilon - phi_(0)` |
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