University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 41 - Quantum Mechanics II: Atomic Structure - Problems - Exercises - Page 1403: 41.35

Answer

See explanation.

Work Step by Step

Equation 41.45 gives the energy of an atomic level, taking screening into account. It is given in terms of n and $Z_{eff}$ by $E_n=-\frac{Z_{eff}^2}{n^2}(13.6 eV)$. Find the effective atomic number for an outer electron. a. Z=4 for Be, so singly-ionized Be has 3 electrons. The electron configuration for $Be^{+}$ is $1s^2 2s$. In this ion, there is one electron outside a set of filled subshells. We assume full screening by the inner-subshell electrons, so there are 4 protons and 2 electrons interior to the 2s electron. $Z_{eff}=4-2=2$ for the 2s electron. $E_{2s}=-\frac{2^2}{2^2}(13.6 eV)= -13.6 eV$ b. Similarly, $Z_{eff}=2$ for the N shell of calcium, where n = 4 for the outermost electron. $E=-\frac{2^2}{4^2}(13.6 eV)= -3.4 eV$
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