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 3.34×1027kg. The deuterons exit the cyclotron with a kinetic energy of 6.40 MeV .

A-What is the speed of the deuterons when they exit?

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

C-If the beam current is 350 A how many deuterons strike the target each second?

Explanation / Answer

m =3.34*10^-27 kg , K =6.4 MeV

A) K =(1/2)mv^2

6.4*10^6*1.6*10^-19 = 0.5*3.34*10^-27*v^2

v =2.48*10^7 m/s

B) centripetal force = magnetic force

mv^2/r =qvB

2mv/d = qB

2*3.34*10^-27*2.48*10^7/d= 1.6*10^-19*1.25

d =0.828 m

C) i =350 uA

i = nq/t

350*10^-6 = n*1.6*10^-19/1

n =2.2*10^15

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