calculate effective nuclear charge for 5s and 4d electron in Ag on basis of Slater rule ?
Answers
Answer:
Slater's rules allow you to estimate the effective nuclear charge Zeff from the real number of protons in the nucleus and the effective shielding of electrons in each orbital "shell" (e.g., to compare the effective nuclear charge and shielding 3d and 4s in transition metals)
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The effective nuclear charge for 5s electron in Silver(Ag) is 4.20 and the effective nuclear charge for 4d electron in Silver(Ag) is 8.20
Given:
Silver (Ag) atom
To Find:
The effective nuclear charge for 5s and 4d electron in Ag.
Solution:
The electronic configuration of Ag is
1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d¹⁰ 4p⁶ 5s² 4d⁹.
Arrange this in shell order,
1s² (2s² 2p⁶) (3s² 3p⁶ 3d¹⁰) (4s² 4p⁶ 4d⁹) 5s²
i) For 5s ---> 1s² (2s² 2p⁶) (3s² 3p⁶ 3d¹⁰) (4s² 4p⁶ 4d⁹) 5s²
no of e⁻,(n) (2) (8) (18) (17) (2)
Shielding value for 5s electron is given as,
σ = ((n-1)x0.35 (5s electron shell)+ (n x 0.85 (inner shell)) + (n x 1.0 (innermost shell))) (n = no of electrons in respective shells)
= ((2-1) x 0.35) + (17x0.85) + (28x1.0)
= 0.35 + 14.45 + 28
= 42.80
The effective nuclear charge is given by, Z* = Z - σ
where, Z - Atomic number
σ - shielding value
The effective nuclear charge for 5s electron is,
Z* = 47 - 42.80
= 4.20
ii) For 4d ---> 1s² (2s² 2p⁶) (3s² 3p⁶ 3d¹⁰) (4s² 4p⁶) 4d⁹
no of e⁻,(n) (2) (8) (18) (8) (9)
For 4d electrons, 5s electrons are neglected because they won't shield inner electrons as they're the outermost.
Shielding value for 4d electron,
σ = ((n-1)x0.35 (4d electron shell) + (n x 1.0 (innermost shell)))
= ((9-1) x 0.35) + (36x1.0)
= 2.80 + 36
= 38.80
The effective nuclear charge is given by, Z* = Z - σ
where, Z - Atomic number
σ - shielding value
The effective nuclear charge for 4d electron is,
Z* = 47 - 38.80
= 8.20
Therefore, The effective nuclear charge for 5s and 4d electrons in Silver(Ag) on basis of the Slater rule is 4.20 and 8.20 respectively.
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