Edge length of a cube is 400 pm. Then its bodydiagonal length would be

Options

A. 600 pm
B. 566pm
C. 693 pm
D. 500 pm

Answer

To find the body diagonal length of a cube with an edge length of 400 pm, follow these steps:

### Step-by-Step Solution:

1. **Identify the edge length of the cube:**
The edge length (a) of the cube is given as 400 pm (picometers).

\[ a = 400 \, \text{pm} \]

2. **Use the formula for the body diagonal of a cube:**
The formula for the body diagonal (d) of a cube in terms of its edge length (a) is:

\[ d = \sqrt{3} \cdot a \]

3. **Substitute the edge length into the formula:**
Now, substitute the value of a into the formula to find the body diagonal:

\[ d = \sqrt{3} \cdot 400 \, \text{pm} \]

4. **Calculate the value:**
First, calculate \(\sqrt{3}\):

\[ \sqrt{3} \approx 1.732 \]

Now, multiply this by 400 pm:

\[ d \approx 1.732 \cdot 400 \, \text{pm} = 692.8 \, \text{pm} \]

Rounding this to three significant figures gives:

\[ d \approx 693 \, \text{pm} \]

5. **Final Answer:**
The body diagonal length of the cube is approximately:

\[ \text{Body Diagonal} \approx 693 \, \text{pm} \]