Cyclotrons are widely used in nuclear medicine for producing short-lived radioactive isotopes. these cyclotrons typically accelerate h− (the hydride ion, which has one proton and two electrons) to an energy of 5mev to 20mev. this ion has a mass very close to that of a proton because the electron mass is negligible−about 1/2000 of the protons mass. a typical magnetic field in such cyclotrons is 1.7 t .

part a

what is the speed of a 5.0-mev h−?

express your answer with the appropriate units.

part b

if the h− has energy 5.0mev and b= 1.7 t , what is the radius of this ions circular orbit?

express your answer with the appropriate units.

(A)

(B)

Explanation:

Given:

(A)

kinetic energy of 5 MeV ion:

(B)

Radius of ion when having energy 5.0 MeV:

We know:

..................................(1)

also,

..........................(2)

where:

F= force on the charge

q= quantity of charge on the particle (an electron in this case)

m= mass of the charged particle

B= magnetic field in which the charge is projected

r= radius of the path circulation of the charge

v= velocity of the charge at the instant

From eq. (1) & (2)

putting the reaspective values:

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explanation:

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