Chemistry
Calculation of Zeff between two elements
Step-by-step chemistry solution: Calculation of Zeff between two elements
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1. What the problem is asking (in plain language)
We have two transition‑metal atoms that have the same d‑electron count and the same s‑electron count, only the principal quantum number of the d‑orbital is different:
| Element | Atomic number ( Z ) | Electron configuration (valence part) |
|---|---|---|
| I | 24 (Cr) | ([Ar]\,3d^{5}\,4s^{1}) |
| II | 42 (Mo) | ([Kr]\,4d^{5}\,5s^{1}) |
The question asks: Which electron feels the larger effective nuclear charge ( (Z_{\text{eff}}) )?
The answer choices were
- a) (Z_{\text{eff}}(\text{II}) > Z_{\text{eff}}(\text{I}))
- b) (Z_{\text{eff}}(\text{II}) < Z_{\text{eff}}(\text{I}))
- c) (Z_{\text{eff}}(\text{II}) = Z_{\text{eff}}(\text{I})) (the correct answer)
The student’s intuition is that a 4d electron is “farther away” from the nucleus than a 3d electron, so it should feel a smaller nuclear attraction. The work below shows why Slater’s rules give the same (Z_{\text{eff}}) for both electrons.
2. Detailed step‑by‑step calculation using Slater’s rules
Slater’s rules give a simple way to estimate the shielding constant S for an electron.
(Z_{\text{eff}} = Z - S)
2.1. Write the electron configuration in Slater’s grouping order
For transition‑metal d electrons we use the following groups (from innermost to outermost):
- ((1s)(2s\,2p)(3s\,3p)(4s\,4p)(5s\,5p)\dots) (whole shells that are lower in (n))
- ((nd\,nf))
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