Final answer:
The volume of a carbon atom is calculated using the volume formula for a sphere, after converting the given radius from picometers to centimeters. The formula V = \( \frac{4}{3}\pi r^3 \) is applied with the converted radius to find the volume in cubic centimeters.
Step-by-step explanation:
The question asks us to calculate the volume of a carbon atom using its given radius. To do this, we apply the formula for the volume of a sphere: V = \( \frac{4}{3}\pi r^3 \), where V is the volume and r is the radius of the atom.
First, we need to convert the radius from picometers (pm) to centimeters (cm), since 1 pm is equal to \(1 \times 10^{-12}\) cm. Thus, the radius of 70 pm becomes 7.0 \times 10^1 \times 10^{-12} cm, or 7.0 \times 10^{-11} cm. Now, we can insert this value into the volume formula:
V = \( \frac{4}{3}\pi (7.0 \times 10^{-11} \text{ cm})^3 \)
Calculating the volume will give us the atom's volume in cubic centimeters (cm³). Since the radius provided pm, we expect the volume to be a small value due to the scale of atomic dimensions.