The density of solid copper (Cu) is 8.96 g/cm^3. How many atoms are present per cubic centimeter (cm^3) of Cu? (Atomic mass of Cu = 63.55 g/mol; Avogadro's number = 6.022 × 10^{23} atoms/mol)

• A. 8.50 × 10^{22} atoms
• B. 8.50 × 10^{21} atoms
• C. 8.50 × 10^{22} atoms
• D. 8.50 × 10^{22} atoms

Answer: (A)

Verified step by step guidance

1. Identify the given data: density of copper (\( \rho = 8.96 \ \text{g/cm}^3 \)), atomic mass of copper (\( M = 63.55 \ \text{g/mol} \)), and Avogadro's number (\( N_A = 6.022 \times 10^{23} \ \text{atoms/mol} \)).
2. Calculate the number of moles of copper in 1 cm\(^3\) using the formula: \[ \text{moles} = \frac{\text{mass}}{\text{molar mass}} = \frac{\rho}{M} \]. Here, mass is the density times the volume (which is 1 cm\(^3\)).
3. Use Avogadro's number to convert moles to atoms: \[ \text{atoms} = \text{moles} \times N_A \].
4. Substitute the values into the equation: \[ \text{atoms per cm}^3 = \left( \frac{8.96}{63.55} \right) \times 6.022 \times 10^{23} \].
5. Perform the arithmetic to find the number of atoms per cm\(^3\) of copper.