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An electron and a photon each have a wavelength of 1.00 nm. Find a. their momenta, b. the energy of the photon, and c. the kinetic energy of electron. |
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Answer» Solution :(a) Both electron and photon have same WAVELENGTH. So, they have same momentum also, `P = (H)/(lambda) = (6.6 xx 10^(-34))/(1 xx 10^(-9)) = 6.6 xx 10^(-25) "kg MS"^(-1)` (b) ENERGY of a photon, `E = (hc)/(lambda) = (6.6 xx 10^(-34) xx 3 xx 10^(8))/(1 xx 10^(-9)) = 19.8 xx 10^(-17)J` `= (19.8 xx 10^(-17))/(1.6 xx 10^(-19)) = 12.375 xx 10^(2) = 1.24 xx 10^(3) eV` E = 1.24 keV (c) Kinetic energy of electron, `K = (p^(2))/(2m)` `= ((6.6 xx 10^(-25))^(2))/(2 xx 9.1 xx 10^(-31)) = (43.56 xx 10^(-50))/(18.2 xx 10^(-31))= 2.39 xx 10^(-19) J` `= (2.39 xx 10^(-19))/(1.6 xx 10^(-19))` K = 1.49 eV |
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