A helium leak detector uses a mass spectrometer to detect tiny leaks in a vacuum

Question

A helium leak detector uses a mass spectrometer to detect tiny leaks in a vacuum chamber. The chamber is evacuated with a vacuum pump and then sprayed with helium gas on the outside. If there is any leak, the helium molecules pass through the leak and into the chamber, whose volume is sampled by the leak detector. In the spectrometer, helium ions are accelerated and released into a tube, where their motion is perpendicular to an applied magnetic field, B rightarrow and they follow a circular orbit of radius r and then hit a detector. Calculate the velocity required if the orbital radius of the ions is to be no more than 9 cm, the magnetic field is 0.16 T, and the mass of a helium-4 atom is about 6.6 times 10-27 kg. Assume that each ion is singly ionized (has one electron less than the neutral atom). By what factor does the required velocity change if helium-3 atoms, which have about 3/4 as much mass as helium-4 atoms, are used?

Explanation / Answer

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