The X-X bond length is `1.00A^(0)` and C-C bond length is `1.54A^(@)`. If electronegativites of 'X' and 'C' are 3.0 and 2.0 respectively, the C-X bond length is likely to be:

Options

A. 1.27Å
B. 1.28Å
C. 1.18Å
D. 1.08Å

Answer

To find the C-X bond length given the bond lengths of X-X and C-C, as well as the electronegativities of the elements involved, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Data**:
- X-X bond length = 1.00 Å
- C-C bond length = 1.54 Å
- Electronegativity of X (χ_X) = 3.0
- Electronegativity of C (χ_C) = 2.0

2. **Calculate Atomic Radii**:
- The bond length is approximately twice the atomic radius for homonuclear diatomic molecules.
- For X:
\[ \text{Radius of X} = \frac{\text{X-X bond length}}{2} = \frac{1.00 \, \text{Å}}{2} = 0.50 \, \text{Å} \]
- For C:
\[ \text{Radius of C} = \frac{\text{C-C bond length}}{2} = \frac{1.54 \, \text{Å}}{2} = 0.77 \, \text{Å} \]

3. **Use the Bond Length Formula**:
- The bond length of C-X can be estimated using the formula:
\[ \text{C-X bond length} = \text{Radius of C} + \text{Radius of X} - 0.09 \times |\chi_X - \chi_C| \]
- Substitute the values:
\[ \text{C-X bond length} = 0.77 \, \text{Å} + 0.50 \, \text{Å} - 0.09 \times |3.0 - 2.0| \]

4. **Calculate the Difference in Electronegativity**:
- The difference in electronegativity:
\[ |\chi_X - \chi_C| = |3.0 - 2.0| = 1.0 \]
- Now, calculate the correction term:
\[ 0.09 \times 1.0 = 0.09 \]

5. **Final Calculation**:
- Substitute back into the bond length formula:
\[ \text{C-X bond length} = 0.77 \, \text{Å} + 0.50 \, \text{Å} - 0.09 \]
\[ = 1.27 \, \text{Å} - 0.09 = 1.18 \, \text{Å} \]

6. **Conclusion**:
- Therefore, the C-X bond length is approximately **1.18 Å**.