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 6.20 MeV .

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

Express your answer with the appropriate units.

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?

Express your answer with the appropriate units.

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

Explanation / Answer

(a) Kinetic energy = 6.20*106*1.6*10-19 J
we know that kinetic energy = (1/2)mV2 where m is the mass and V is the velocity
V = 2.437*107 m/s
(b) Magnetic field = 1.25 T
charge on the deutron = 1.6*10-19 C
FOrce due to magnetic field = qVB
Force due to centripetal force = mV2 / R where R is radius of path
qVB = mV2 /R
R = mV/q = 3.34*10-27*2.437*107 / (1.6*10-19) = 5.087*10-1 = 0.5087 m
(c) Current = 350*10-6 A
we know that
current = Charge/time
charge = current*time
here time = 1 second
therefore charge = 350*10-6 C
One deutron have q = 1.6*10-19 C
therefore
number of deutrons strike the target = 350*10-6 /1.6*10-19 = 218.75*1013

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