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Effective nuclear charge for the 4s electron in 19 K is

Question

Effective nuclear charge for the 4s electron in 19 K is

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Solution

The effective nuclear charge (Zeff) for an electron can be calculated using Slater's rules.

  1. Write the electron configuration for the atom. For potassium (K), the electron configuration is 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹.

  2. According to Slater's rules, each electron in the same shell (n=4) contributes 0.35 to the shielding, each electron in the n-1 shell contributes 0.85, and each electron in the n-2 or lower shells contributes 1.00.

  3. Calculate the shielding constant (S) by adding up the contributions from all the electrons. For potassium, S = (0.350) + (0.852) + (1.00*18) = 20.7.

  4. The effective nuclear charge is then calculated by subtracting the shielding constant from the atomic number (Z). For potassium, Zeff = Z - S = 19 - 20.7 = -1.7.

However, this result is not physically meaningful, as the effective nuclear charge cannot be negative. This discrepancy arises because Slater's rules are an approximation and do not always give accurate results. A more accurate method for calculating the effective nuclear charge would be to use quantum mechanical calculations.

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