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) given the interatomic distances for carbon (C) and silicon-carbon pairs, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Interatomic Distance**:
The interatomic distance between two atoms is the distance from the center of one atom to the center of the other atom. For two identical atoms (like C-C), the interatomic distance (D) is equal to twice the atomic radius (R) of the atom.

2. **Calculate the Atomic Radius of Carbon (C)**:
- Given the interatomic distance for C-C is 154 pm.
- Since both atoms are carbon, we can express this as:
\[ D_{C-C} = 2R_C \]
- Therefore, the radius of carbon (R_C) can be calculated as:
\[ R_C = \frac{D_{C-C}}{2} = \frac{154 \text{ pm}}{2} = 77 \text{ pm} \]

3. **Set Up the Equation for Si-C Interatomic Distance**:
- Given the interatomic distance for Si-C is 188 pm.
- The relationship between the atomic radii of silicon (R_Si) and carbon (R_C) can be expressed as:
\[ D_{Si-C} = R_C + R_{Si} \]
- Substituting the known values:
\[ 188 \text{ pm} = R_C + R_{Si} \]
- We already found that \( R_C = 77 \text{ pm} \).

4. **Solve for the Atomic Radius of Silicon (R_Si)**:
- Rearranging the equation gives:
\[ R_{Si} = D_{Si-C} - R_C = 188 \text{ pm} - 77 \text{ pm} \]
- Calculating this gives:
\[ R_{Si} = 111 \text{ pm} \]

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

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