The C - C and Si - C interatomic distances are 154 pm and 188 pm. The atomic radius of Si is

Options

A. 77 pm
B. 94 pm
C. 114 pm
D. 111 pm

Answer

To find the atomic radius of silicon (Si) based on the given interatomic distances, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Interatomic Distances**:
- The C-C interatomic distance is given as 154 pm.
- The Si-C interatomic distance is given as 188 pm.

2. **Calculate the Atomic Radius of Carbon (C)**:
- The C-C bond distance represents the sum of the radii of two carbon atoms. Therefore, we can express this as:
\[ 2R_C = 154 \text{ pm} \]
- To find the radius of one carbon atom (R_C), we divide the total distance by 2:
\[ R_C = \frac{154 \text{ pm}}{2} = 77 \text{ pm} \]

3. **Set Up the Equation for Si-C Bond**:
- The Si-C bond distance represents the sum of the radius of silicon (R_Si) and the radius of carbon (R_C):
\[ R_Si + R_C = 188 \text{ pm} \]

4. **Substitute the Known Value of R_C**:
- We already calculated R_C as 77 pm. Substitute this value into the equation:
\[ R_Si + 77 \text{ pm} = 188 \text{ pm} \]

5. **Solve for the Atomic Radius of Silicon (R_Si)**:
- Rearranging the equation to find R_Si:
\[ R_Si = 188 \text{ pm} - 77 \text{ pm} = 111 \text{ pm} \]

6. **Conclusion**:
- The atomic radius of silicon (Si) is 111 pm.

### Final Answer:
The atomic radius of silicon is **111 pm**.

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