Polonium adopts cubic structure with edge length of cube being 0.336 nm. The distance of the body diagonal is

Options

A. 0.336 nm
B. 0.291 nm
C. 0.582 nm
D. 0.481 nm

Answer

To find the distance of the body diagonal of a cubic structure given the edge length, we can follow these steps:

### Step-by-Step Solution

1. **Understand the Geometry of the Cube**:
- A cube has edges of equal length. The body diagonal connects two opposite corners of the cube.

2. **Identify the Given Information**:
- The edge length (a) of the cube is given as 0.336 nm.

3. **Use the Pythagorean Theorem**:
- The body diagonal (d) of a cube can be calculated using the formula:
\[ d = \sqrt{a^2 + a^2 + a^2} = \sqrt{3a^2} = \sqrt{3} \cdot a \]

4. **Substitute the Value of Edge Length**:
- Now, substitute the value of a into the formula:
\[ d = \sqrt{3} \cdot 0.336 \, \text{nm} \]

5. **Calculate the Value**:
- First, calculate \(\sqrt{3}\):
\[ \sqrt{3} \approx 1.732 \]
- Now multiply:
\[ d \approx 1.732 \cdot 0.336 \, \text{nm} \approx 0.5819 \, \text{nm} \]

6. **Round the Result**:
- Rounding to three decimal places gives:
\[ d \approx 0.582 \, \text{nm} \]

7. **Final Answer**:
- The distance of the body diagonal is approximately **0.582 nm**.