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 in a cubic structure, we can use the following steps:

### Step 1: Understand the Geometry of the Cube
In a cube, the body diagonal connects two opposite corners of the cube. If the edge length of the cube is denoted as \( a \), the body diagonal can be calculated using the Pythagorean theorem in three dimensions.

### Step 2: Use the Formula for the Body Diagonal
The formula for the length of the body diagonal \( d \) of a cube with edge length \( a \) is given by:
\[ d = a \sqrt{3} \]

### Step 3: Substitute the Given Edge Length
Given that the edge length \( a = 0.336 \, \text{nm} \), we can substitute this value into the formula:
\[ d = 0.336 \, \text{nm} \times \sqrt{3} \]

### Step 4: Calculate the Value of \( \sqrt{3} \)
The value of \( \sqrt{3} \) is approximately \( 1.732 \).

### Step 5: Perform the Calculation
Now, we can calculate the body diagonal:
\[ d = 0.336 \, \text{nm} \times 1.732 \approx 0.581 \, \text{nm} \]

### Final Answer
The distance of the body diagonal of the polonium cube is approximately \( 0.581 \, \text{nm} \).

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