Ions with a v0 enter a spectrometer through an opening to a uniform magnetic fie

Question

Ions with a v0 enter a spectrometer through an opening to a uniform magnetic field region B, where they follow a semicircular path to the other opening on the top. The distance d between the entry opening and the exit opening is 1.6m

These ions have a mass of 35 amu (1 amu = 1.66x10^-27 kg), with a charge of +1e when they enter the spectrometer.If the magnitude of the magnetic field B is .222T

A)What should be the ions velocity of entry for them to go out through the other opening?

B)What should be the ions kinetic energy for them to go out through the other opening?

Explanation / Answer

Part A)

Apply r = mv/qB

(.8) = (35)(1.66 X 10^-27)(v)/(1.6 X 10^-19)(.222)

v = 4.89 X 10^5 m/s

Part B)

KE = .5mv^2

KE = (.5)(35)(1.66 X 10^-27)(4.89 X 10^5)^2

KE = 6.95 X 10^-15 Joules

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