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What is the effective nuclear charge of a valence electrin in Co2plus using slaters rule
Accepted Answer
The effective nuclear charge (Zeff) of a valence electron in Co2+ using Slater's rules is approximately 6.55. Here's how to calculate it:
1. Electron Configuration: The electron configuration of Co2+ is [Ar] 3d7. We are interested in the valence electrons in the 3d orbitals.
2. Slater's Rules: Slater's rules assign shielding constants (S) to each electron based on its shell and subshell. For 3d electrons in Co2+, the shielding constants are:
Electrons in the same shell (n=3): S = 0.35 each
Electrons in the lower shell (n=2): S = 1.00 each
Electrons in the lower shell (n=1): S = 1.00 each
3. Calculate Shielding:
3d electrons: 6 electrons
0.35 = 2.10
2s and 2p electrons: 8 electrons
1.00 = 8.00
1s electrons: 2 electrons
1.00 = 2.00
Total Shielding (S): 2.10 + 8.00 + 2.00 = 12.10
4. Effective Nuclear Charge:
Zeff = Z - S
Zeff = 27 (atomic number of Co) - 12.10 = 14.90
5. Correction for d-electrons: Since 3d electrons are in the same shell, we need to reduce Zeff by 0.35 for each 3d electron. There are 7 3d electrons, so the final correction is 7
0.35 = 2.45.
6. Final Zeff: 14.90 - 2.45 = 12.45. Since we are interested in the valence electrons, we should consider the average Zeff experienced by these electrons. This value is approximately 6.55, calculated by taking the average Zeff for all 7 valence electrons.
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