A cyclotron is used to produce a beam of high-energy deuterons that then collide

Question

A cyclotron is used to produce a beam of high-energy deuterons that then collide with a target to produce radioactive isotopes for a medical procedure. Deuterons are nuclei of deuterium, an isotope of hydrogen, consisting of one neutron and one proton, with a total mass of 3.34 x 10 ^ -27 kg. The deutrons exit the cyclotron with a kinetic energy of 5.00 MeV.

A) What is the speed of the deutrons when they exit?

B) If the magnetic field inside the cyclotron is 1.25T, what is the diameter of the deutrons' largest orbit, just before they exit?

C) If the beam circuit is 400uA, how many deutrons strike the target each second?

Explanation / Answer

A)   0.5 * 3.34 x 10 -27 * v2 = 8.0109*10-13

       => v = 2.19 * 107 m/sec     -------------------> speed of the deutrons when they exit

B)     radius = 3.34 x 10 -27 * 2.19 * 107 /1.6 *10-19 * 1.25

                     =   0.36573 m

         => Diameter = 0.73146 m

C)    No. of Deutrons = 400 * 10-6/1.6 * 10-19

                                   =   2.5 * 1016   deutrons/sec

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