Physics: Principles with Applications (7th Edition)

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

Chapter 30 - Nuclear Physics and Radioactivity - Problems - Page 882: 45

Answer

Seven $\alpha$ particles and four $\beta^{-}$ particles were emitted.

Work Step by Step

Only the $\alpha$ emissions decrease the mass number (by 4 each time, because of the loss of 2 protons and 2 neutrons). The mass number changes from 235 to 207, a decrease of 28. There must have been seven $\alpha$ particles emitted. With each $\alpha$ particle emitted, the atomic number decreases by 2 (because of the loss of 2 protons and 2 neutrons). Considering only the alpha particles emitted, the atomic number would have decreased from 92 to 78. When a $\beta^{-}$ particle is emitted, the atomic number rises by 1 (because of the emitted negative particle). Since the final atomic number is not 78, but 82, there must have been four $\beta^{-}$ particles emitted.
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