While tuning up a medical cyclotron for use in isotope
Chapter 44, Problem 44.53(choose chapter or problem)
While tuning up a medical cyclotron for use in isotope production, you obtain the data given in the table.
B is the uniform magnetic field in the cyclotron, and \(K_{\max }\) is the maximum kinetic energy of the particle being accelerated, which is a proton. The radius R of the proton path at maximum kinetic energy has the same value for each magnetic-field value. (a) Compare the kinetic energy values in the table to the rest energy \(m c^{2}\) of a proton. Is it necessary to use relativistic expressions in your analysis? Explain. (b) Graph your data as \(K_{\max }\) versus \(B^{2}\). Use the slope of the best-fit straight line to your data to find R. (c) What is the maximum kinetic energy for a 0.25-T magnetic field? (d) What is the angular frequency \(\omega\) of the proton when B = 0.40 T?
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