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Derive de Broglie equation and give its significance. |
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Answer» Solution :(1)Louis de Boglie extended the concept of dual nature of light to all form of matter.To quantufy this relation,he derived an equation for the wavelength of a matter WAVE. (2)He combined the following two equations of energy of which one represents wave charater(hv) and the other represents the particle nature `(MC^(2))`. Planck.s quantum hypothesis: E=hv.......(1) Einsteins mass-energy relationship: `E=mc^(2)`...............(2)From (1) and (2) hv=`mc^(2)` `hc/gamma=mc^(2)` `therefore gamma=mc^(2)`...........(3) THe equation (3) represents the wavelength of photons whose momentum is given by mc.(Photons have zero rest mass.) (3)For a particle of mater with mass m and moving with a VELOCITY v,the equation(3) can be written as`gamma=h/(MV)`...........(4) (4)This is valid only when the particle travels at speed much less than the speed of light. (5)This equation implies that a moving particle can be considered as wave and a wave can exhibit the properties of a particle(i.e.momentum). (6)Significance of de BROGLIE equation: For a particle with high liner momentum,the wavelength will be too small cannot be observed,For a microscpic particle such as an electron,the mass is `9.1xx10^(-31)`kg.Hence the wavelength is much larger than the size of atom and it becomes significant. |
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