Effective nuclear charge for the 4s electron in 19K is
Question
Effective nuclear charge for the 4s electron in 19K is
Solution
The effective nuclear charge (Zeff) for an electron can be calculated using Slater's rules.
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Write the electron configuration for the atom. For potassium (19K), the electron configuration is 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹.
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Determine the number of core and valence electrons. In potassium, there are 18 core electrons and 1 valence electron (in the 4s orbital).
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Calculate the shielding constant (S) using Slater's rules. For a 4s electron, each electron in the same shell (n=4) contributes 0.35 to S, each electron in the n=3 shell contributes 0.85, and each electron in shells with n<3 contributes 1.00. In potassium, there are no other electrons in the n=4 shell, 8 electrons in the n=3 shell, and 10 electrons in shells with n<3. So, S = (00.35) + (80.85) + (10*1.00) = 6.8 + 10 = 16.8.
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Calculate the effective nuclear charge using the formula Zeff = Z - S, where Z is the atomic number. For potassium, Z = 19, so Zeff = 19 - 16.8 = 2.2.
So, the effective nuclear charge for the 4s electron in potassium is approximately +2.2.
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