Chemistry: The Central Science (13th Edition)

Published by Prentice Hall
ISBN 10: 0321910419
ISBN 13: 978-0-32191-041-7

Chapter 7 - Periodic Properties of the Elements - Exercises: 7.15d

Answer

Neither of the two methods of approximation accounts for the gradual increase in $Z_{eff}$ as we move down a group.

Work Step by Step

Both approaches produce 2 equal estimates of $Z_{eff}$ of Na and K ($1+$ and $2.2+$), so it only concerns with the number of electrons and the nuclear charge. The gradual increase in $Z_{eff}$ as we move down a group is caused by the more spread the electrons are, or the positions of the electrons. None of the two approaches account for that.
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