27.20     Cyclotrons are widely used in nuclear medicine for producing short-lived radioactive isotopes.  These cyclotrons typically accelerate H− (the hydride ion, which has one proton and two electrons) to an energy of 5 MeV to 20 MeV.  This ion has a mass very close to that of a proton because the electron mass is negligible—about 1/2000 of the proton’s mass.  A typical magnetic field in such cyclotrons is 1.9 T.  (a) What is the speed of a 5.0-MeV H−?  (b) If the H− has energy 5.0 MeV and B = 1.9 T, what is the radius of this ion’s circular orbit?

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Asked Oct 21, 2019

27.20     Cyclotrons are widely used in nuclear medicine for producing short-lived radioactive isotopes.  These cyclotrons typically accelerate H (the hydride ion, which has one proton and two electrons) to an energy of 5 MeV to 20 MeV.  This ion has a mass very close to that of a proton because the electron mass is negligible—about 1/2000 of the proton’s mass.  A typical magnetic field in such cyclotrons is 1.9 T.  (a) What is the speed of a 5.0-MeV H?  (b) If the H has energy 5.0 MeV and B = 1.9 T, what is the radius of this ion’s circular orbit?

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Write the expression for the kinetic energy of the proton, that is the equivalent to the energy ...

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