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 value of silicon given its covalent radius of 1.175 Å, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Formula**:
We use the formula for calculating electronegativity (EN):
\[ \text{EN} = 0.359 \times \frac{Z_{\text{effective}}}{r^2} + 0.7441 \]
where \(Z_{\text{effective}}\) is the effective nuclear charge and \(r\) is the covalent radius.

2. **Determine the Covalent Radius**:
Given that the covalent radius \(r\) of silicon is \(1.175 \, \text{Å}\).

3. **Calculate \(Z_{\text{effective}}\)**:
- Silicon has an atomic number of 14, which means it has 14 protons.
- The electronic configuration of silicon is \(1s^2 2s^2 2p^6 3s^2 3p^2\).
- To find the shielding effect, we need to consider the electrons in the inner shells:
- The \(1s\), \(2s\), and \(2p\) electrons shield the outer electrons.
- The shielding effect can be calculated as follows:
- For \(1s\) (2 electrons): contributes 0.35
- For \(2s\) (2 electrons): contributes 0.35
- For \(2p\) (6 electrons): contributes 0.85
- For \(3s\) (2 electrons): contributes 1.0
- For \(3p\) (2 electrons): contributes 1.0
- Total shielding effect = \(2 \times 0.35 + 6 \times 0.85 + 2 \times 1.0\)
- Calculate:
\[ \text{Shielding effect} = 0.70 + 5.10 + 2.0 = 7.80 \]
- Now, calculate \(Z_{\text{effective}}\):
\[ Z_{\text{effective}} = Z - \text{Shielding effect} = 14 - 7.80 = 6.20 \]

4. **Substitute Values into the Formula**:
Now substitute \(Z_{\text{effective}} = 6.20\) and \(r = 1.175\) into the electronegativity formula:
\[ \text{EN} = 0.359 \times \frac{6.20}{(1.175)^2} + 0.7441 \]

5. **Calculate \(r^2\)**:
\[ (1.175)^2 = 1.380625 \]

6. **Calculate the Fraction**:
\[ \frac{6.20}{1.380625} \approx 4.49 \]

7. **Calculate the First Part of the Formula**:
\[ 0.359 \times 4.49 \approx 1.60791 \]

8. **Add the Constant**:
\[ \text{EN} = 1.60791 + 0.7441 \approx 2.35201 \]

9. **Final Result**:
The electronegativity value of silicon is approximately **2.35**.