based on slater's rule, what is the shielding constant experienced by a valance d- electron in a copper atom

The shielding constant of a d electron in copper is 22.15.

From Slaters's rule;

Zeff = Z - S

Where;

Z = Nuclear charge

S = Shielding constant

Now we are required to find the shielding constant for copper d - electrons;

The shielding contributed by the d electrons = (9 × 0.35) = 3.15

The shielding contributed by other electrons = (19 × 1.00) = 19

Total shielding constant =  3.15 + 19 = 22.15

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The general principle behind Slater's Rule is that the actual charge felt by an electron is equal to what you'd expect the charge to be from a certain number of protons, but minus a certain amount of charge from other electrons. 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). Slater's rules are fairly simple and produce fairly accurate predictions of things like the electron configurations and ionization energies.

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