Singly ionized uranium atoms are sent through a mass spectrometer. The electric

Question

Singly ionized uranium atoms are sent through a mass spectrometer. The electric field between the plates of the voltage selector is set to 1000 V/m. The magnetic field between the plates of the voltage selector is set to 1.15 T and is directed along the negative z-axis. Upon entering the chamber, the ions encounter a magnetic field with a strength of 2.2 T, but directed in the same direction as the magnetic field in the velocity selector. Two isotopes of uranium are in the sample being tested, U-235 & U-238. How far apart are they when they land in the collector in the chamber?

Explanation / Answer

speed of ions = E / B = 1000 / 1.15 = 869.57 m/s

radius of turn in chamber:

       r = m v / q B

for U235, m = 235 * 1.67x10^-27

for U238, m = 238 * 1.67x10^-27

So now

for U235   r = (235* 1.67x10^-27) * 869.57 / 1.60x10^-19 * 2.2 = 0.96949 mm

for U238    r = (238* 1.67x10^-27) * 869.57 / 1.60x10^-19 * 2.2 = 0.98187 mm

I dont have the diagram for your problem, but I believe they turn in half a circle. So they are separated by two times the difference in their radius. Or

separation = 2 (0.98187 - 0.96949) = 0.02476 mm = 2.476 x 10^-5 meters

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