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What is the radius of the orbit of an electron

  1. Feb 11, 2016 #1

    Hi All,

    Having difficultly figuring out where I've gone wrong with this problem. Any guidance gratefully received.

    1. The problem statement, all variables and given/known data


    A 4.76 keV electron (an electron that has a kinetic energy equal to 4.76 keV) moves in a circular orbit that is perpendicular to a magnetic field of 0.392 T.

    i) Find the radius of the orbit.

    2. Relevant equations

    KE = 0.5 m v^2

    r = mv / qB (where r = radius, m = mass of electron, q = charge of electron and B = magnetic field)

    3. The attempt at a solution

    Given the KE and the mass, find the velocity v. KE = 4.76 x 10^3 eV and m = 9.109x10^-31 kg

    v = sqrt ( (2xKE / m))

    v = sqrt ( (2x(4.76x10^3)/9.109 x 10^-31))

    v= 1.02 x 10^17 m/s

    Now having found the velocity v, find the radius r.

    r = mv / qB

    r = (9.109x10^-31)(1.02 x 10^17) / (1.602x10^-19)(0.392)

    r = 1.48 x 10^6 m

    However this answer is wrong and I don't know where I'm going wrong. Any help greatfully recieved.
     
  2. jcsd
  3. Feb 11, 2016 #2

    gneill

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    Staff: Mentor

    Compare the velocity you found to the speed of light. Does it make sense? :wink:
     
  4. Feb 11, 2016 #3
    Now that you mention it, it's a rather daft velocity.

    1) I'm sure I'm using the right formula : KE = .5 (m) v ^2
    2) The rearrangement to obtain v on the LHS looks correct: v = sqrt ( (2xKE / m))
    3) And the calculation is correct : v = sqrt ( (2x(4.76x10^3)/9.109 x 10^-31))
    4) So it leads me to think that I have the wrong value for the energy of the electron in the formula which is generating such a large velocity. So there is some transformation I need to do to 4.76x10^eV....

    However after looking back at my books and notes, I can't figure this one out.

    Could you please push me in the right direction. A good strong shove would be appreciated :-)
     
  5. Feb 11, 2016 #4

    gneill

    User Avatar

    Staff: Mentor

    Shove: While the eV is indeed an energy unit, 1 eV ≠ 1 J . Look up its definition.
     
  6. Feb 11, 2016 #5
    Thank you for that shove.

    I misunderstood eV. I see the definition is : 1eV = 1.602 x 10^-19 J.
    I should be using Joules for KE.

    v = sqrt ( (2x(4.76x10^3 * 1.602x10^-19 )/9.109 x 10^-31))

    v = 4.09 x 10^7 m/s

    which is still about 13% of the speed of light, so rather fast...

    Is this correct now?
     
  7. Feb 11, 2016 #6

    gneill

    User Avatar

    Staff: Mentor

    Yup. Much better! :approve:
     
  8. Feb 12, 2016 #7
    Thank you very much, that was really very helpful.
    I've a much better understanding of what I was doing wrong now.
     
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