Edge length of cube is 300 pm. Its body diagonal would be:

Options

A. 600 pm
B. 423 pm
C. `519.6 "pm"`
D. `450.5 "pm"`

Explanation

To find the body diagonal of a cube with an edge length of 300 pm (picometers), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Geometry of the Cube**:
- A cube has equal edge lengths. If the edge length is denoted as \( a \), then all sides of the cube are \( a \).

2. **Identify the Formula for the Body Diagonal**:
- The body diagonal \( d \) of a cube can be calculated using the formula:
\[ d = \sqrt{a^2 + a^2 + a^2} = \sqrt{3a^2} \]
- This simplifies to:
\[ d = a\sqrt{3} \]

3. **Substitute the Given Edge Length**:
- Given that the edge length \( a = 300 \) pm, substitute this value into the formula:
\[ d = 300 \sqrt{3} \]

4. **Calculate \( \sqrt{3} \)**:
- The approximate value of \( \sqrt{3} \) is \( 1.732 \).

5. **Perform the Multiplication**:
- Now calculate the body diagonal:
\[ d = 300 \times 1.732 = 519.6 \text{ pm} \]

6. **Final Result**:
- Therefore, the body diagonal of the cube is approximately \( 519.6 \) pm.

### Final Answer:
The body diagonal of the cube is **519.6 pm**.

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