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
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.