(adsbygoogle = window.adsbygoogle || []).push({}); 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 mv^{2}

F = mv^{2}/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.}

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# Homework Help: Energy of a cyclotron

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