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Speed of an electron

  1. Jun 20, 2007 #1
    I have a question here where a potential difference is applied to a stationary electron. I have calculated the energy translated to the electron already and I know the mass energy of the electron.

    If I want to find its final speed I assume that I use a rearrangement of the relativistic formula? And if so, what value would I use for Energy? Would it simply be the total energy : mass energy + translated energy?

    Thanks for any help
     
    Last edited: Jun 20, 2007
  2. jcsd
  3. Jun 20, 2007 #2

    malawi_glenn

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    There are many formulas you can use,

    [tex] E_{tot} = E_{k} + mc^{2} = \gamma mc^{2} [/tex]

    [tex] \gamma = \dfrac{1}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} [/tex]

    remember that you can not take the rest mass of the electron in the expression of the kinetic energy.
     
    Last edited: Jun 20, 2007
  4. Jun 20, 2007 #3
    Would that be Ek as in translated kinetic energy?
     
  5. Jun 20, 2007 #4

    malawi_glenn

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    Well E_k is kinetic energy, what you mean by "translated kinetic energy" I do not know.

    You can also use this:


    (E_tot)^2 = (pc)^2 + (mc^2)^2

    where p is the momentum:
    p = gamma * mv, v is velocity.

    And from this we can get:

    v = c * sqrt[1 - (mc^2 / E_tot)^2 ]
     
  6. Jun 20, 2007 #5
    I see... So if I have calculated the kinetic energy of an electron to be for example 6 x 10^-12J, then I can calculate the total energy as

    (6 x 10^-12J) + mass of electron * speed of light^2 ?

    And once this is established I can use one of the formulas to give me v?
     
    Last edited: Jun 20, 2007
  7. Jun 20, 2007 #6

    malawi_glenn

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    How did you calculate the kinetic energy of electron?

    You took:

    Potential (electrical) energy = qV, where V is the electric poteintal, and then
    qV = Kinetic energy?

    Well then it is ok, and if you want to find out the velocity of the electron, you must calculate relativistic. (if the kinetic energy is approx 10% or more of the rest mass energy of electron)
     
  8. Jun 20, 2007 #7
    yes thats exactly it.... potential difference(100V) x charge of electron(q).

    I understand that relativistic formulas are used when the particles speed become close to the speed of light. Is this right? Otherwise the classic Newtonian formula 1/2 mv^2 can be used?
     
  9. Jun 20, 2007 #8

    malawi_glenn

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    yes, as I said, when the kinetic energy is apporx 10% or more, it may be good to use relativistic. The bigger the E_k is compared to the rest mass, the better to use the relativistic =)
     
  10. Jun 20, 2007 #9
    Many thanks for your assistance
     
  11. Jul 20, 2007 #10
    Hi there, sorry if this sounds like a noob question but why can't you use Newtonian formula at speeds close to c :confused:
     
  12. Jul 20, 2007 #11

    malawi_glenn

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