The unit cell of Cr metal is cubic and contains 2 atoms. If the density of Cr= 7.19 Mg/m3; determine the dimension of Cr unit cell

Answer 1

To determine the dimension of the Cr unit cell, we first need to calculate the molar mass of chromium (Cr), which is 51.996 g/mol.

Next, we need to convert the density of Cr from Mg/m3 to g/cm3, which is 7.19 g/cm3.

Then, we can use the formula for density to find the volume of the unit cell:

Density = mass/volume

Volume = mass/density

Using the molar mass of Cr, we can calculate the mass of one Cr atom:

51.996 g/mol = x g/1 mol

x = 51.996 g/mol

Since there are 2 atoms in the unit cell:

Mass = 2 * 51.996 g/mol = 103.992 g/mol

Now we can calculate the volume of the unit cell:

Volume = 103.992 g/mol / 7.19 g/cm3 = 14.45 cm3

Since the unit cell is cubic, all sides are of equal length. The dimension of the unit cell is the cube root of the volume:

V = l3

l = ∛V

l = ∛14.45 cm3 ≈ 2.32 cm

Therefore, the dimension of the Cr unit cell is approximately 2.32 cm.