Question

The shielding constant of a 2p electron (calculated using Slater's rules) is

• A. 3.30
• B. 3.45
• C. 4.55
• D. 2.45

Hint:

When applying Slater's rules, be careful not to count the electron for which you are calculating the shielding. For an electron in the (ns, np) group, all other electrons in that same group contribute 0.35.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Slater's rules provide a method for estimating the effective nuclear charge (\(Z_{eff}\)) felt by an electron. The effective nuclear charge is the actual nuclear charge (Z) minus a shielding constant (\(\sigma\)), which represents the screening effect of other electrons. \(Z_{eff} = Z - \sigma\). The question asks for the value of \(\sigma\) for a 2p electron. Since the atom is not specified, we must test a few common atoms to see which one yields one of the given options.
Step 2: Key Formula or Approach:
According to Slater's rules for an electron in an ns or np orbital:
1. Group the electronic configuration: (1s) (2s, 2p) (3s, 3p) (3d) etc.
2. Electrons in the same (ns, np) group contribute 0.35 each to \(\sigma\).
3. Electrons in the (n-1) shell contribute 0.85 each.
4. Electrons in shells (n-2) or lower contribute 1.00 each.
Step 3: Detailed Explanation:
Let's calculate \(\sigma\) for a 2p electron in an Oxygen atom (O, Z=8).
The electronic configuration of Oxygen is 1s\(^2\) 2s\(^2\) 2p\(^4\).
We group it according to Slater's rules: (1s\(^2\)) (2s\(^2\) 2p\(^4\)).
We are calculating the shielding for one of the 2p electrons.
Electrons in the same group (2s, 2p): There are 2 electrons in 2s and 3 other electrons in 2p. Total = 2 + 3 = 5 electrons.
Their contribution to \(\sigma\) is \(5 \times 0.35 = 1.75\).
Electrons in the (n-1) shell (1s): There are 2 electrons in the 1s shell.
Their contribution to \(\sigma\) is \(2 \times 0.85 = 1.70\).
Step 4: Final Answer:
The total shielding constant \(\sigma\) is the sum of the contributions:
\[ \sigma = 1.75 + 1.70 = 3.45 \] This value matches option (2).