p39_057 - the momentum p and kinetic energy K are related...

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57. (a) The momentum of the photon is given by p = E/c ,where E is its energy. Its wavelength is λ = h p = hc E = 1240 eV · nm 1 . 00 eV = 1240 nm . See Exercise 3. The momentum of the electron is given by p = 2 mK ,wh e r e K is its kinetic energy and m is its mass. Its wavelength is λ = h p = h 2 mK . According to Exercise 49, if K is in electron volts, this is λ = 1 . 226 nm · eV 1 / 2 K = 1 . 226 nm · eV 1 / 2 1 . 00 eV =1 . 23 nm . (b) For the photon, λ = hc E = 1240 eV · nm 1 . 00 × 10 9 eV =1 . 24 × 10 6
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Unformatted text preview: the momentum p and kinetic energy K are related by ( pc ) 2 = K 2 + 2 Kmc 2 . Thus, pc = p K 2 + 2 Kmc 2 = p (1 . 00 10 9 eV) 2 + 2(1 . 00 10 9 eV)(0 . 511 10 6 eV) = 1 . 00 10 9 eV . The wavelength is = h p = hc pc = 1240 eV nm 1 . 00 10 9 eV = 1 . 24 10 6 nm ....
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