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Figure P32.70 shows a mass spectrometer, an analytical instrument used to identify the various molecules in a sample by measuring their...

Figure P32.70 shows a mass spectrometer, an analytical instrument used to identify the various molecules in a sample by measuring their charge-to-mass ratio e/m. The sample is ionized, the positive ions are accelerated (starting from rest) through a potential difference ΔV, and they then enter a region of uniform magnetic field. The field bends the ions into circular trajectories, but after just half a circle they either strike the wall or pass through a small opening to a detector. As the accelerating voltage is slowly increased, different ions reach the detector and are measured. Typical design values are a magnetic field strength B = 0.160 T and a spacing between the entrance and exit holes d = 6.50 cm. Calculate the accelerating potential difference ΔV required to detect each of the ions listed below. The accuracy of your answers should reflect the accuracy of the data given below. (Although N2+ and CO+ both have a nominal molecular mass of 28, they are easily distinguished by virtue of their unique potential differences.)
Atomic masses
12C 12.0000 u
14N 14.0031 u
16O 15.9949 u



Figure P32.70
(a) N2+ 1 V
(b) O2+ 2 V
(c) CO+ 3 V

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