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: 59

Answer

It might be a hydrogen-2 nucleus (i.e., a deuteron) or a helium-4 nucleus (i.e., an alpha particle).

Work Step by Step

The particle is undeflected in the crossed fields. Its speed is given by the velocity selector equation, v = E/B. (Section 20–11). If the electric field is removed, the particle travels in a circular path. Calculate the mass of the particle using Newton’s second law. $$qvB=ma=m\frac{v^2}{r}$$ $$m=\frac{qBr}{v}=\frac{qBr}{(E/B)} $$ We know that the charge q must be an integer multiple of the elementary charge, q = (N)(e). $$m=\frac{NeB^2r}{E}$$ $$m=\frac{N(1.6\times10^{-19}C)(0.034T)^2(0.027m)}{1500V/m}$$ $$=N(3.3\times10^{-27}kg)\approx N(2.0u)$$ The particle has an atomic mass that is a multiple of 2.0 u. It might be a hydrogen-2 nucleus (i.e., a deuteron) or a helium-4 nucleus (i.e., an alpha particle).
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