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 - Questions - Page 582: 23

Answer

See answer. The doubly-ionized ion strikes the film at a distance that is half that of the singly-ionized ion.

Work Step by Step

All ions emerge from the velocity selector at the same speed, because v = E/B, independent of charge or mass. Once the ions enter the uniform-magnetic-field portion of the mass spectrometer, where the field has strength B’, they begin to follow a circular path. At that point, the difference in their charges starts to matter. Equation 20–12 (page 578) for the mass spectrometer relates the mass to the charge, field strength, radius of the path, and the ions’ speed. $$m=\frac{qB’r}{v}$$ This can be solved for the radius. $$r=\frac{mv}{qB’}$$ On the right hand side of the equation, the charge q is the only quantity that differs between the single and doubly-charged ions. The doubly-ionized ions travel in a semi-circular path that is half the radius of the path traveled by the singly-ionized ions. The doubly-ionized ions strike the film at a distance that is half that of the singly-ionized ions.
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