Which form of iron has a higher density?

• A. Face-centered cubic (fcc) iron
• B. Hexagonal close-packed (hcp) iron
• C. Body-centered cubic (bcc) iron

Answer: (A)

Verified step by step guidance

1. Understand that the density of a crystalline form depends on how atoms are packed in the unit cell and the mass of atoms per unit volume.
2. Recall the three crystal structures mentioned: Face-centered cubic (fcc), Hexagonal close-packed (hcp), and Body-centered cubic (bcc), each with a characteristic atomic packing factor (APF).
3. Note the atomic packing factors: fcc and hcp both have an APF of approximately 0.74 (meaning 74% of the volume is occupied by atoms), while bcc has a lower APF of about 0.68.
4. Since density \( \rho \) is given by \( \rho = \frac{Z \times M}{N_A \times V_c} \), where \(Z\) is the number of atoms per unit cell, \(M\) is molar mass, \(N_A\) is Avogadro's number, and \(V_c\) is the volume of the unit cell, a higher packing efficiency (higher APF) generally leads to higher density if the atomic mass is constant.
5. Compare the fcc and hcp structures: both have similar packing efficiencies, but differences in unit cell volume and arrangement can slightly affect density; however, both are denser than bcc iron due to the lower packing efficiency of bcc.