Physics: Principles with Applications (7th Edition)

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

Chapter 31 - Nuclear Energy; Effects and Uses of Radiation - Problems - Page 912: 45

Answer

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Work Step by Step

The two definitions of the roentgen are: i. $1.6\times10^{12}$ ion pairs/gram of dry air produced by the radiation ii. $0.878\times10^{-2}J$ of energy deposited per kg of air. Start with definition (ii) and relate the two definitions by the value of 35 eV needed to produce an ion pair. $$1\;R=\frac{0.878\times10^{-2}J}{kg}\frac{1kg}{1000g}\frac{1\;eV}{1.60\times10^{-19}J}\frac{ion\;pair}{35eV}$$ $$1.57\times10^{12}\frac{ion\;pair}{g}$$ The number of ion pairs produced per gram of dry air is about $2\%$ away from that of definition (i), making the two definitions very consistent.
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