Using the appropriate relativistic relations between energyand momentum, find an

Question

Using the appropriate relativistic relations between energyand momentum, find and compare the wavelengths of electrons andphotons at the three different kinetic energies: 1 keV, 1 MeV, 1GeV

Answer:
Energy            Electron              Photon 1keV              0.0388nm            1.24mnm 1MeV            870fm                 1240fm 1GeV             1.239fm               1.240fm   I know how to get the electron wavelength for 1 keV and I knowhow to get the photon wavelength for all the energies, but for somereason I can't get the right answer for the electron wavelengthsfor 1 MeV and 1 GeV. I don't know what I'm doing wrong. Cansomeone plese help me out? Thank you. Using the appropriate relativistic relations between energyand momentum, find and compare the wavelengths of electrons andphotons at the three different kinetic energies: 1 keV, 1 MeV, 1GeV

Answer:
Energy            Electron              Photon 1keV              0.0388nm            1.24mnm 1MeV            870fm                 1240fm 1GeV             1.239fm               1.240fm   I know how to get the electron wavelength for 1 keV and I knowhow to get the photon wavelength for all the energies, but for somereason I can't get the right answer for the electron wavelengthsfor 1 MeV and 1 GeV. I don't know what I'm doing wrong. Cansomeone plese help me out? Thank you.

Explanation / Answer

mass of electron m = 9.11*10-31kg
For K = 1MeV = 1.6*10-13J p= sqrt[[(1.6*10-13J)/(3*108m/s)]2+2(1.6*10-13J)(9.11*10-31kg)]    = sqrt[2.84*10-43+2.9152*10-43 ] kgm/s    = 7.586*10-22kgm/s
Then wavelength = h/p       =(6.626*10-34Js)/(7.586*10-22kgm/s)       =8.7*10-13m       =870*10-15m       = 870fm
For K = 1GeV = 1.6*10-10J p= sqrt[[(1.6*10-10J)/(3*108m/s)]2+2(1.6*10-10J)(9.11*10-31kg)]    =sqrt[2.84*10-37 +2.9152*10-40 ]kgm/s    = 5.33*10-19kgm/s
Then wavelength = h/p       =(6.626*10-34Js)/(5.33*10-19kgm/s)       =1.239*10-15m         = 1.239fm For K = 1MeV = 1.6*10-13J p= sqrt[[(1.6*10-13J)/(3*108m/s)]2+2(1.6*10-13J)(9.11*10-31kg)]    = sqrt[2.84*10-43+2.9152*10-43 ] kgm/s    = 7.586*10-22kgm/s
Then wavelength = h/p       =(6.626*10-34Js)/(7.586*10-22kgm/s)       =8.7*10-13m       =870*10-15m       = 870fm
For K = 1GeV = 1.6*10-10J p= sqrt[[(1.6*10-10J)/(3*108m/s)]2+2(1.6*10-10J)(9.11*10-31kg)]    =sqrt[2.84*10-37 +2.9152*10-40 ]kgm/s    = 5.33*10-19kgm/s
Then wavelength = h/p       =(6.626*10-34Js)/(5.33*10-19kgm/s)       =1.239*10-15m         = 1.239fm For K = 1GeV = 1.6*10-10J p= sqrt[[(1.6*10-10J)/(3*108m/s)]2+2(1.6*10-10J)(9.11*10-31kg)]    =sqrt[2.84*10-37 +2.9152*10-40 ]kgm/s    = 5.33*10-19kgm/s
Then wavelength = h/p       =(6.626*10-34Js)/(5.33*10-19kgm/s)       =1.239*10-15m         = 1.239fm

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