Final answer:
The atomic radius of barium in a body-centered cubic crystal structure can be calculated using the edge length of the unit cell and the geometric formula for BCC lattices, resulting in an approximate atomic radius of 0.725 Å for barium.
Step-by-step explanation:
To calculate the atomic radius of barium in a body-centered cubic (BCC) crystal structure, we use the edge length provided and the geometric relationships inherent in BCC lattices. In a BCC lattice, the diagonal running from one corner of the cube to the opposite corner (through the center) is equal to the cube edge length times the square root of 3.
This body diagonal equals four atomic radii because it passes through two radii in the center atom and touches the centers of the atoms at each end of the diagonal. Therefore, the atomic radius (r) is equal to the edge length (a) divided by 4 times the square root of 3.
Using this formula for barium with an edge length (a) of 5.025 Å:
r = (5.025 Å) / (4∙√3)
r ≈ 5.025 Å / 6.9282
r ≈ 0.725 Å