Final answer:
The radius of an atom in a body-centered cubic unit cell can be found using the edge length and is approximately 140 pm if the given edge length is 324 pm.
Step-by-step explanation:
To calculate the radius of an atom in a body-centered cubic unit cell (bcc), we need to understand the geometric relationship between the edge length of the cell and the radius of the atoms.
In a bcc unit cell, the body diagonal is equal to √3 times the edge length (a), and this diagonal is also equal to 4 times the radius of the atom (r) that's present at each corner and at the center of the unit cell.
So, if we know the edge length, we can find the radius using the formula r = a√3/4.
However, it appears there's a misunderstanding in your question: the radius of a body can't be measured in cubic centimeters (cm³) because that's a unit of volume, and the radius is a linear measure.
If we assume you meant that the edge length of the bcc cell is 3.24 x10⁻²³ cm (which is 324 pm since 1 cm = 10±² pm). Then, r = (3.24 x 10⁻¸ cm) √3 / 4
= (324 pm) √3 / 4
≈ 140 pm.
So, the radius of the atom would be approximately 140 picometers (pm).