The metal nickel crystallizes in a face centered cubic structure. Its density is `8.90 gm//cm^(3)`. Calculate (a) the length of the edge of a unit cell. (b) the radius of nickel atom. (atomic weight of Ni = 58.89).

Answer

To solve the problem step by step, we will calculate the length of the edge of the unit cell and the radius of the nickel atom based on the given information.

### Given Data:
- Density of nickel (ρ) = 8.90 g/cm³
- Atomic weight of nickel (M) = 58.89 g/mol
- Nickel crystallizes in a face-centered cubic (FCC) structure.

### Step 1: Determine the number of atoms per unit cell (Z)
In a face-centered cubic (FCC) structure, the number of atoms per unit cell (Z) is 4. This is calculated as follows:
- There are 8 corner atoms, each contributing 1/8 of an atom to the unit cell (8 * 1/8 = 1).
- There are 6 face-centered atoms, each contributing 1/2 of an atom to the unit cell (6 * 1/2 = 3).
- Therefore, Z = 1 + 3 = 4.