Barium has a radius of 224 pm and crystallizes in a body-centered cubic structure. What is the edge length of the unit cell?
edge=4r/sqrt3 in bcc
thank you :)
To find the edge length of the unit cell, we need to first recall the relationship between the radius of an atom and the edge length of a unit cell in a body-centered cubic (BCC) structure.
In a BCC structure, the atoms are arranged in a cube shape with atoms at the eight corners and one atom at the center of the cube. The atoms touch along the body diagonal of the cube.
For a BCC structure, the relationship between the edge length (a) and the atomic radius (r) can be expressed as:
a = 4 * r / √3
Given that the radius of barium (Ba) is 224 pm, we can substitute this value into the formula:
a = 4 * 224 pm / √3
To simplify the calculation, we will convert picometers (pm) to angstroms (Å) since 1 Å = 100 pm:
a = 4 * 224 pm / √3
≈ 4 * 2.24 Å / √3
≈ 8.96 Å / √3
To get the final answer, we can approximate the value of √3 as 1.732:
a ≈ 8.96 Å / 1.732
Now we can calculate the approximate edge length of the unit cell:
a ≈ 5.17 Å