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Item 8

Part A

What is the speed of the deuterons when they exit?

Express your answer with the appropriate units.

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Part 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.

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Part C

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

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Item 8

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 6.10 MeV .

You may want to review ( pages 778 - 783) .

Part A

What is the speed of the deuterons when they exit?

Express your answer with the appropriate units.

v =

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Part 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.

d =

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Part C

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

Q = deuetrons

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Explanation / Answer

kinetic energy K = 6.1 MeV = 6.1*10^6*1.6*10^-19 J

Kinetic energy K = (1/2)*m*v^2

(1/2)*3.34*10^-27*v^2 = 6.1*10^6*1.6*10^-19

v = 2.42*10^6 m/s

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In the magnetic field

the magnetic force provides necessary centripetal force

Fb = Fc

q*v*B = m*v^2/R

radius R = m*v/(q*B)

R = (3.34*10^-27*2.42*10^6)/(1.25*1.6*10^-19)

R = 0.0404 m

======================================

Q*q = I

Q = I/q

Q = 350*10^-6/(1.6*10^-19)

Q = 2.2*10^15 deuterons

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