What will be the value of screening constant `(sigma)` for the sodium atom?

Answer

To determine the value of the screening constant (σ) for the sodium atom, we will follow these steps:

### Step 1: Understand the Concept of Screening Constant (σ)
The screening constant (σ) is a measure of the extent to which inner electrons shield outer electrons from the full charge of the nucleus. It is calculated based on the number of electrons in different shells and their contributions to shielding.

**Hint:** Remember, the outermost electrons are not considered for their own shielding.

### Step 2: Identify the Atomic Number and Electronic Configuration of Sodium
Sodium (Na) has an atomic number of 11. Its electronic configuration is:
\[ \text{1s}^2 \, \text{2s}^2 \, \text{2p}^6 \, \text{3s}^1 \]

**Hint:** The outermost shell for sodium is the 3s shell.

### Step 3: Determine the Contribution of Electrons in Each Shell
- **Outermost shell (3s):** The outermost electrons do not contribute to their own screening, so the contribution to σ from the 3s electron is 0.
- **Second shell (2s and 2p):** There are 8 electrons (2 from 2s and 6 from 2p). The screening constant per electron for the n-1 shell (where n=3) is 0.85. Therefore, the total contribution from the second shell is:
\[ \text{Contribution from 2s and 2p} = 8 \times 0.85 = 6.8 \]

**Hint:** Use the formula \( \text{Total Contribution} = \text{Number of Electrons} \times \text{Screening Constant per Electron} \).

### Step 4: Calculate the Contribution from the First Shell (1s)
For the first shell (1s), there are 2 electrons, and the screening constant per electron for n-2 (where n=3) is 1. Thus, the contribution from the first shell is:
\[ \text{Contribution from 1s} = 2 \times 1 = 2 \]

**Hint:** Remember to adjust the shell number when calculating contributions from inner shells.

### Step 5: Sum Up All Contributions to Get the Total Screening Constant (σ)
Now, we can sum the contributions from all shells:
\[ \sigma = \text{Contribution from 3s} + \text{Contribution from 2s and 2p} + \text{Contribution from 1s} \]
\[ \sigma = 0 + 6.8 + 2 = 8.8 \]

### Final Answer
The value of the screening constant (σ) for the sodium atom is **8.8**.

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