Vanadium crystallizes in a body-centered cubic lattice and the density is 5.96g/cm3 what is the unit cell edge length in pm?

The correct answer is 305 pm

Explanation:

The density of a unit cell (d) is given by the following equation:

Where M is the molar mass, Nₐ is the Avogadro number (6.023 x 10²³ atom/mol), a is the edge of unit cell and z is the number of atoms per unit cell. We have to determine the edge of the unit cell (a) and we know the molar mass from the Periodic Table (M= 50.9415) and the density (d= 5.96 g/cm³). For BCC, z= 2 atom. So, we introduce the data in the equation and we determine a:

⇒

a= 3.05 x 10⁻⁸ cm= 3.05 x 10⁻¹⁰ m

We need the value in pm, so we convert from m to pm (1 pm= 10⁻¹²m):

3.05 x 10⁻¹⁰m x 1 pm/10⁻¹²m= 305.03 pm= 305 pm