Effective Nuclear Charge Video Lessons

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Problem: Calculate Zeff for the 4s electron in a copper atom, Cu.Effective nuclear charge, Zeff, is defined asZeff = Z − Swhere ZZ is true nuclear charge and SS is the amount of shielding. In 1930, John C. Slater devised the following set of empirical rules to estimate SS for a designated ns or np electron:i. Write the electron configuration of the element, and group the subshells as follows: (1s), (2s, 2p), (3s, 3p), (3d), (4s, 4p), (4d), (4f ), (5s, 5p), and so on. ii Electrons in groups to the right of the (ns np) group contribute nothing to the shielding constant for the designated electroniii. 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 is in an nd or nf group, rules (i), (ii), and (iii) remain the same but rules (iv) and (v) are replaced by the following: vi. Each electron in a group lying to the left of the nd or nf group contributes 1.00 to the shielding constant. These rules are a simplified generalization based on the average behavior of different types of electrons.

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Calculate Zeff for the 4s electron in a copper atom, Cu.


Effective nuclear charge, Zeff, is defined as

Zeff = Z − S

where ZZ is true nuclear charge and SS is the amount of shielding. 

In 1930, John C. Slater devised the following set of empirical rules to estimate SS for a designated ns or np electron:

i. Write the electron configuration of the element, and group the subshells as follows: (1s), (2s, 2p), (3s, 3p), (3d), (4s, 4p), (4d), (4f ), (5s, 5p), and so on. 

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 is in an nd or nf group, rules (i), (ii), and (iii) remain the same but rules (iv) and (v) are replaced by the following: 

vi. Each electron in a group lying to the left of the nd or nf group contributes 1.00 to the shielding constant. These rules are a simplified generalization based on the average behavior of different types of electrons.

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