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Energy of a cyclotron

  1. Sep 6, 2010 #1
    1. The problem statement, all variables and given/known data
    Prove that the energy of a cyclotron can be expressed as:

    E (MeV) = 4.8e-3 (B * R * q)2/A

    Where B is the magnetic field in Tesla
    R is the maximum radius of the cyclotron in cm.
    q is the charge of the particle accelerated.
    A - is the mass number.

    We can ignore relativistic effects.



    2. Relevant equations

    T = 1/2 mv2

    F = mv2/R = qvB. Solve for v and plug in to kinetic energy formula T

    v = qBR/m



    3. The attempt at a solution

    We can plug in v into T to get kinetic energy expressed in q, B, R, and m:

    T = 1/2 * (qBR)2/m

    Now, need to express m in terms of mass number.

    We know that N (the number of particles) = 6.02e23 (particles/mole)/A(g/mole) * m

    Let N = 1 since we're only interested in what the energy of a particle in the cyclotron.
    Solving for m: m = A / 6.02e23.

    Plugging in m in equation for T:

    T = 1/2 * (qBR)2 * 6.02e23/A

    Now we need to add conversion factors for getting A from g/mole to kg/mole. Also need to convert from Joules to MeV. Finally need to get R from meters to cm. This gives me:

    T = 1/2 * (qBR)2 * 6.02e23/A * 1000g/kg * (100 cm/1m)2 * 1.6e-13 MeV/J

    This gives me 4.816e17 MeV - which is not correct.

    In order to get R in cm, should I convert to cgs units first? If so, then I need to convert the magnetic field from Guass to Tesla.

    Thanks for you help.
     
  2. jcsd
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