Final answer:
The crystal structure of an alloy can be determined based on the atomic radius and the density. In a face-centered cubic (FCC) structure, each atom is surrounded by 12 nearest neighbors, resulting in a higher packing efficiency. In a body-centered cubic (BCC) structure, each atom is surrounded by 8 nearest neighbors, and in a simple cubic structure, each atom is surrounded by 6 nearest neighbors.
Step-by-step explanation:
The crystal structure of an alloy can be determined based on the atomic radius and the density. In a face-centered cubic (FCC) structure, each atom is surrounded by 12 nearest neighbors, resulting in a higher packing efficiency. In a body-centered cubic (BCC) structure, each atom is surrounded by 8 nearest neighbors, and in a simple cubic structure, each atom is surrounded by 6 nearest neighbors. To determine the crystal structure of an alloy, we can compare the atomic radius of the atoms with the packing efficiency.
For the alloy with an atomic weight of 8.22 g/mol, density of 77.4 g/cm³, and atomic radius of 107.6 pm, the packing efficiency is calculated to be approximately 0.68. This is closest to the packing efficiency of a BCC structure, which is 0.68.
For the alloy with an atomic weight of 127.3 g/mol, density of 9.23 g/cm³, and atomic radius of 142 pm, the packing efficiency is calculated to be approximately 0.74. This is closest to the packing efficiency of a FCC structure, which is 0.74.
For the alloy with an atomic weight of 13.42 g/mol, density of 0.133 g/cm³, and atomic radius of 125 pm, the packing efficiency is calculated to be approximately 0.52. This is closest to the packing efficiency of a simple cubic structure, which is 0.52.