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1. A mass spectrometer is a device for measuring the mass of charged ions that are first accelerated by an electric field, and then travel in circular orbits in a uniform magnetic field. Lets assume the chamber at the lower left contains hydrogen gas, but may have some contaminants. The gas is ionized in positively charged atomic ions that are accelerated through a voltage drop V. The ions then enter a region with uniform magnetic field B that points into the page. The spectrometer measures the radii R of the circular orbits of the ions using detectors located on the left wall of the vacuum chamber. The ionic charge is denoted q = ze where is an integer. The maximum positive charge an ion can have is Ze where Z is the atolnic number; 2-1 is hydrogen, Z=2 is helium etc. R2 (a) If an ion has mass m and charge ze, what is the speed of the ion (b) Derive the radius of the orbit R of an ion with charge ze, mass m, (c) Use your results in (a) and (b) to derive a relation between the quan- after it has been accelerated through a voltage drop V? and speed v in magnetic field B tities R, V, B, m, e, and (d) You first calibrate the spectrometer by using the radius of the orbit for protons (z = Z = 1). Protons have a mass of 1.672621898 x 10-27 kg and charge e = 1.6021766208 x 10-19C. You carefully tune
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