What is the radius (in cm) of a pure copper sphere that contains 1.14 * 10^24 copper atoms? [The volume of a sphere is (4/3)πr^3 and the density of copper is 8.96 g/cm^3.]

Verified step by step guidance

1. Calculate the molar mass of copper (Cu) using the periodic table, which is approximately 63.55 g/mol.
2. Determine the number of moles of copper atoms by dividing the given number of atoms (1.14 \times 10^{24}) by Avogadro's number (6.022 \times 10^{23} atoms/mol).
3. Calculate the mass of copper using the number of moles and the molar mass: \text{mass} = \text{moles} \times \text{molar mass}.
4. Use the density formula to find the volume of the copper sphere: \text{volume} = \frac{\text{mass}}{\text{density}}.
5. Solve for the radius of the sphere using the volume formula for a sphere: \text{volume} = \frac{4}{3}\pi r^3, and rearrange to find r.