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Miscalculation with speeds of electrons?

  1. Oct 9, 2005 #1
    for the following question:
    how much work (in MeV) must be done to increase the speed of an electron from 1.2*10^8 m/s to 2.4*10^8 m/s?

    my problem:
    E= (gamma)mc^2=m(c^2){1/[1-(2.4/30^2]-1/[1-(1.2/30^2]}
    =0.511(c^2)[1/(0.6)-1/(0.84)^(1/2)]=2.65*10^16

    the correct answer should be 0.294 MeV~

    does anybody know what went wrong?
     
  2. jcsd
  3. Oct 9, 2005 #2

    Andrew Mason

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    [tex]\Delta E = (\gamma_2 - \gamma_1)m_ec^2[/tex]

    [tex]\gamma_1 = (1-v_1^2/c^2)^{-1/2} = 1.091[/tex]
    [tex]\gamma_2 = (1-v_2^2/c^2)^{-1/2} = 1.667[/tex]
    [tex]m_ec^2 = .511 Mev[/tex]

    [tex]\Delta E = .576 * .511 = .294 MeV[/tex]

    AM
     
    Last edited: Oct 9, 2005
  4. Oct 9, 2005 #3
    i think i'm missing something...
    [tex]m_ec^2 = .511 Mev[/tex]
    i thought that [tex]m_e[/tex]=0.511?
     
  5. Oct 9, 2005 #4

    Doc Al

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    [itex]m_e[/itex] is the mass of the electron: [itex]9.11 \ 10^{-31}[/itex] kg. If you calculate [itex]m_e c^2[/itex] in standard units, you'll get the answer in Joules. Then convert Joules to eV. (1 eV = [itex]1.60 \ 10^{-19}[/itex] J.)
     
  6. Oct 9, 2005 #5

    Andrew Mason

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    When mass is written in terms of an energy, it is understood that it is in units of Energy/c^2. The 1/c^2 is often omitted when it is written, so it can be confusing. So, [itex]m_e = .511 Mev/c^2[/itex] and [itex]m_ec^2 = .511 MeV[/itex].

    AM
     
  7. Oct 10, 2005 #6
    my math is crummy...
    um, isn't units and the numbers multiplied separately?
    so m=(0.511*c^2) MeV?
     
  8. Oct 10, 2005 #7

    Andrew Mason

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    Well, the units are really MeV/(9e16 m^2/sec^2) which works out to 1.78e-30 kilograms. But kilograms is not a very useful unit when measuring the mass of an electron. So we just use units of MeV/c^2 or MeV-mass

    [tex]m \ne .511 c^2 MeV[/tex]

    [tex]m = .511 (MeV/c^2) units = .511 MeV(mass) [/tex]
    [tex] = .511e6/9e16 eV/m^2/sec^2 = .511e6/9e16 *1.6e(-19) kg[/tex]

    AM
     
    Last edited: Oct 10, 2005
  9. Oct 10, 2005 #8
    thank you!!! :)
     
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