Physics: Principles with Applications (7th Edition)

Published by Pearson
ISBN 10: 0-32162-592-7
ISBN 13: 978-0-32162-592-2

Chapter 20 - Magnetism - Problems - Page 586: 60

Answer

2.5 m.

Work Step by Step

The charged particles in the mass spectrometer trace a semicircular path (Figure 20–41). The desired separation of the molecules, on the film, is 0.50 mm. The distance between where a particle enters, and where it strikes the film, is 2r. So, the difference in path radii for the two molecules is 0.25 mm. $$qvB=ma=m\frac{v^2}{r}$$ Note that q, B, and v are the same, so the ratio m/r is the same for the two molecules. $$\frac{m}{r}=\frac{qB}{v}$$ $$\frac{m_{CO}}{r_{CO}}=\frac{m_{N_2}}{r_{N_2}}$$ $$\frac{28.0106u}{r}=\frac{28.0134}{r+2.5\times10^{-4}m}$$ $$r=2.5m$$
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