Copper (Cu) has atomic number $Z = 29$ and electronic configuration $[Ar] 3d^{10} 4s^1$.

The effective nuclear charge ($Z_{\text{eff}}$) represents the net positive charge experienced by an electron. It's calculated using $Z_{\text{eff}} = Z - S$, where $Z$ is the atomic number and $S$ is the shielding constant derived from Slater's rules.

Calculating $Z_{\text{eff}}$ for 4s Electron in Cu

Using Slater's rules for a 4s electron:

• Shielding from $n-1$ shell ($3s^2, 3p^6, 3d^{10}$; 18 electrons) at 0.85 each: $18 \times 0.85 = 15.3$.
• Shielding from $n-2$ shell ($2s^2, 2p^6$; 8 electrons) at 1.00 each: $8 \times 1.00 = 8.0$.
• Shielding from $n-3$ shell ($1s^2$; 2 electrons) at 1.00 each: $2 \times 1.00 = 2.0$.

Total shielding $S = 15.3 + 8.0 + 2.0 = 25.3$.

Thus, $Z_{\text{eff}}(4s) = 29 - 25.3 = 3.70$.

$Z_{\text{eff}}$ Value for 3d Electron in Cu

For the 3d electron in Copper, the calculation based on the relevant rules yields $Z_{\text{eff}}(3d) = 7.85$.

Final Values for Cu Atom

The effective nuclear charge ($Z_{\text{eff}}$) for the 3d and 4s electrons in a Cu atom are 7.85 and 3.70, respectively.

This matches Option C.