Problem 24.30-MC 8 of 10> Constants Part A A cyclotron is used to produce a beam

Question

Problem 24.30-MC 8 of 10> Constants Part A 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 x 10-2 kg. The deuterons exit the cyclotron with a kinetic energy of 6.10 MeV What is the speed of the deuterons when they exit? Express your answer using three significant figures and with the appropriate units. View Available Hint(s) Value Units Submit 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 using three significant figures and with the appropriate units. View Available Hint(s) Value Units Submit

Explanation / Answer

1)

Ek = (1/2) mv^2,

isolate for velocity: v=sqrt(2Ek/m)

where Ek = 6.10 MeV * 1.602*10^-19 J

v = 2.419*10^7 m/s

2)

centripital force is mv^2/r,

we also know that the only force present in the system is the force caused by the magnetic field, qv x B,

therefore

mv^2/r = qvB,

where q is the charge of one proton

r = mv/qB  

r = (3.34*10^-27*2.419*10^7)/(1.602*10^-19*1.25)

d = 2r = 0.806 m

3)

I=q/t

since t = 1s, I = q.

Therefore the total charge that strikes the target each second is 360 microcoulomb.

NUMBER of the deuterons,

so divide that total charge by each charge of a deuteron (which is the same as the charge of a proton) and get

360*10^-6/(1.602*10^-19)

deuterons = 2.247*10^15

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