Physics: Principles with Applications (7th Edition)

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

Chapter 28 - Quantum Mechanics of Atoms - Problems - Page 827: 40

Answer

Chromium.

Work Step by Step

Use the equation developed in Example 28-7 (page 818) to calculate the wavelength of the $K_{\alpha}$ line. $$\frac{1}{\lambda}=(1.097\times10^7m^{-1})(Z-1)^2(\frac{1}{(n’)^2}-\frac{1}{n^2})$$ The wavelength is inversely proportional to $(Z-1)^2$. $$\frac{\lambda_{unknown}}{\lambda_{Fe}}=\frac{(Z_{Fe}-1)^2}{(Z_{unknown}-1)^2}$$ $$Z_{unknown}=((26-1)\sqrt{\frac{194pm}{229pm}})+1=24$$ The unknown material has Z=24, and corresponds to chromium.
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