If the covalent radius of silicon is `1.175 Å` then its elec-tronegativity value is

Options

A. `1.73 `
B. `3.28 `
C. 1.14 `
D. `0.99`

Answer

To find the electronegativity of silicon given its covalent radius of 1.175 Å, we will use the LRED Rocco equation. Here’s a step-by-step solution:

### Step 1: Understand the LRED Rocco Equation
The LRED Rocco equation for calculating electronegativity (X) is given by:
\[ X = \frac{0.359 \times Z_{\text{effective}}}{r^2} + 0.744 \]
where:
- \( Z_{\text{effective}} \) = effective nuclear charge
- \( r \) = covalent radius in Ångströms

### Step 2: Determine the Atomic Number of Silicon
Silicon (Si) has an atomic number \( Z = 14 \).

### Step 3: Calculate the Effective Nuclear Charge (\( Z_{\text{effective}} \))
The effective nuclear charge can be calculated using the formula:
\[ Z_{\text{effective}} = Z - S \]
where \( S \) is the shielding constant.

### Step 4: Calculate the Shielding Constant (\( S \))
Using Slater's rules, we can calculate \( S \):
- For the last electron in the 3rd shell (3s and 3p), we consider the contributions:
- Electrons in the same shell (3s and 3p): 3 electrons contribute \( 0.35 \) each.
- Electrons in the previous shell (2s and 2p): 8 electrons contribute \( 0.85 \) each.
- Electrons in the first shell (1s): 2 electrons contribute \( 1 \) each.

Calculating \( S \):
- Contribution from 3s and 3p: \( 3 \times 0.35 = 1.05 \)
- Contribution from 2s and 2p: \( 8 \times 0.85 = 6.8 \)
- Contribution from 1s: \( 2 \times 1 = 2 \)

Thus,
\[ S = 1.05 + 6.8 + 2 = 9.85 \]

### Step 5: Calculate \( Z_{\text{effective}} \)
Now substituting the values:
\[ Z_{\text{effective}} = 14 - 9.85 = 4.15 \]

### Step 6: Substitute Values into the LRED Rocco Equation
Now substituting \( Z_{\text{effective}} \) and \( r \) into the LRED Rocco equation:
\[ X = \frac{0.359 \times 4.15}{(1.175)^2} + 0.744 \]

### Step 7: Calculate \( r^2 \)
Calculating \( r^2 \):
\[ (1.175)^2 = 1.380625 \]

### Step 8: Calculate \( X \)
Now substituting \( r^2 \) into the equation:
\[ X = \frac{0.359 \times 4.15}{1.380625} + 0.744 \]
Calculating \( 0.359 \times 4.15 = 1.48985 \):
\[ X = \frac{1.48985}{1.380625} + 0.744 \]
Calculating \( \frac{1.48985}{1.380625} \approx 1.080 \):
\[ X \approx 1.080 + 0.744 = 1.824 \]

### Step 9: Final Result
Thus, the electronegativity value of silicon is approximately:
\[ \text{Electronegativity of Silicon} \approx 1.82 \]

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