The density of an unknown metal is 8.94 g/cm^3 and its atomic radius is 0.126 nm. It has a face-centered cubic lattice.

Are you sure you:

1) Typed the subject correctly?
2) Typed the whole question?

To determine the atomic mass of the unknown metal, we need to use the given density and atomic radius.

1. First, let's convert the atomic radius from nanometers (nm) to centimeters (cm). There are 1 x 10^-7 cm in 1 nm. Therefore, the atomic radius is 0.126 nm * 1 x 10^-7 cm/nm = 1.26 x 10^-8 cm.

2. The face-centered cubic (FCC) lattice has 4 atoms per unit cell. In FCC, the atoms are located at the corners of the unit cell and in the center of each face.

3. The volume of the unit cell can be calculated using the formula V = a^3, where "a" is the edge length of the unit cell. In an FCC lattice, the diagonal of the face is equal to 4 times the atomic radius (2√2a = 4r). Therefore, the edge length is equal to the diagonal of the face divided by √2 (a = 2r/√2).

4. Substituting the value of the atomic radius (1.26 x 10^-8 cm) into the equation, we get a = 2(1.26 x 10^-8 cm) / √2 = 1.26 x 10^-8 cm / √2 = 8.92 x 10^-9 cm.

5. The volume of the unit cell (V) can be calculated by V = a^3 = (8.92 x 10^-9 cm)^3 = 7.56 x 10^-25 cm^3.

6. Now, let's calculate the mass of the unit cell. Since the density (ρ) is given in grams per cubic centimeter (g/cm^3), we can use the formula: mass = density * volume.

mass = 8.94 g/cm^3 * 7.56 x 10^-25 cm^3 = 6.76 x 10^-24 g.

7. Since there are 4 atoms per unit cell, the average mass per atom is equal to the mass of the unit cell divided by the number of atoms, which is: average mass per atom = mass / 4.

average mass per atom = 6.76 x 10^-24 g / 4 = 1.69 x 10^-24 g.

Therefore, the atomic mass of the unknown metal is approximately 1.69 x 10^-24 grams.