Step 1: Concept Overview:
Slater's rules estimate the effective nuclear charge (\(Z_{eff}\)) on an electron, calculated as the actual nuclear charge (Z) minus a shielding constant (\(\sigma\)). The screening effect of other electrons is represented by \(\sigma\), and the formula is \(Z_{eff} = Z - \sigma\). The problem asks for \(\sigma\) for a 2p electron. Without a specific atom, we'll test common ones.
Step 2: Key Formula:
Slater's rules for an ns or np electron:
1. Group the electronic configuration: (1s) (2s, 2p) (3s, 3p) (3d) etc.
2. Electrons in the same (ns, np) group contribute 0.35 to \(\sigma\).
3. Electrons in the (n-1) shell contribute 0.85.
4. Electrons in shells (n-2) or lower contribute 1.00.
Step 3: Calculation Example:
Calculate \(\sigma\) for a 2p electron in Oxygen (O, Z=8).
Oxygen's electronic configuration: 1s\(^2\) 2s\(^2\) 2p\(^4\).
Group according to Slater's rules: (1s\(^2\)) (2s\(^2\) 2p\(^4\)).
Calculate shielding for one 2p electron.
Electrons in the (2s, 2p) group: 2 (2s) + 3 (other 2p) = 5 electrons.
Contribution to \(\sigma\): \(5 \times 0.35 = 1.75\).
Electrons in the (n-1) shell (1s): 2 electrons.
Contribution to \(\sigma\): \(2 \times 0.85 = 1.70\).
Step 4: Answer:
Total shielding constant \(\sigma\):
\[ \sigma = 1.75 + 1.70 = 3.45 \]This matches option (2).