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 total mass 3.34 times 10^-27 kg. The deuterons exit the cyclotron with a kinetic energy of 3.60 MeV. If the magnetic field inside the cyclotron is 1.25 T, what is the diameter of the deuterons' largest orbit, just before they exit? Express your answer using three significant figures and with the appropriate units. If the beam current is 450 mu A how many deuterons strike the target each second? Express your answer using throe significant figures.

Explanation / Answer

b) v=sqrt(2Ek/m)

v = sqrt(2*5.77*10^-13/3.34*10^-27) = 1.86*10^7 m/s

mv^2/r=qvB

r=mv/qB

d = 2r = 2*3.34*10^-27*1.86*10^7/1.6*10^-19*1.25

d = 0.62 m

c) q = it = 450*10^-6 C

q = ne

n = 450*10^-6/1.6*10^-19

n = 2.8*10^15

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