Concept explainers
We have seen that the wave functions of hydrogen-like atoms contain the nuclear charge Z for hydrogen-like atoms and ions, but modified through equation (9.3) to account for the phenomenon of shielding or screening. In 1930, John C. Slater devised the following set of empirical rules to calculate a shielding constant for a designated electron in the orbital ns or np:
i. Write the electron configuration of the element, and group the subshells as follows: (1s), (2s, 3p), (3d), (4s, 4p), (4d), (40, (ss, Sp), etc.
ii. Electrons in groups to the right of the (ns, np) group contribute nothing to the shielding constant for the designated electron.
iii. All the other electrons in the (ns, np) group shield the designated electron to the extent of 0.35 each.
iv. All electrons in the n - 1 shell shield to the extent of 0.85 each.
v. All electrons in the n - 2 shell, or lower, shield completely-their contributions to the shielding constant are 1.00 each. When the designated electron being shielded is in an nd or nf group, rules (ii) and (iii) remain the same but rules (iv) and (v) are replaced
by
vi. Each electron in a group lying to the left of the nd or nfgroup contributes 1.00 to the shielding constant.
These rules are a simplified generalization based on the average behavior of different types of electrons. use these rules to do the following:
a. Calculate
b. Calculate
c. Calculate
d. Evaluate the
e. Evaluate
f. Using the radial functions given in Table 8.2 and
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