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A cyclotron operates with an oscillator frequency of 10 MHz. If each dee has a radius of 60 cm, what kinetic energy does the accelerated proton beam acquire?

1. 3.421 MeV
2. 4.421 MeV
3. 5.421 MeV
4. 7.421 MeV

Correct answer: 7.421 MeV

Solution

Using B = 2*pi*m*f/q, KE = (B^2 q^2 r^2)/(2m) = 2*pi^2*m*r^2*f^2 = 2*pi^2*(1.67e-27)*(0.6)^2*(1e7)^2 = 1.19e-12 J = about 7.42 MeV.

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