Final answer:
To calculate the radius of a nickel atom, we use the edge length of the nickel's face-centered cubic unit cell and apply the relationship between the face diagonal and the atom's radii. The calculated radius of a nickel atom is approximately 0.1248 x 10⁻· cm.
Step-by-step explanation:
Calculating the Radius of a Nickel Atom
To calculate the radius of a nickel atom, we must understand the crystalline structure of nickel. Given the edge length of the unit cell for nickel (0.3524 nm) and the density (8.90 g/cm³), we can determine if nickel crystallizes in a simple cubic structure. Since nickel atoms arrange themselves in a face-centered cubic (fcc) structure rather than a simple cubic structure, we can use this information to calculate the atomic radius of nickel.
In a face-centered cubic structure, each unit cell consists of four atoms. Using the edge length (a) and the equation for the diagonal across a face (\(\sqrt{2} imes a\)), we can find the radius (r) since the diagonal is also equal to four radii in a fcc structure (\(4r = \sqrt{2} imes a\)).
Let's execute the calculation:
Therefore, the approximate radius of a nickel atom is 0.1248 × 10⁻· cm.