Vanadium crystallizes in a body-centred cubic structure and has an atomic radius of 131 pm.Determine the density of vanadium if the edge length of a bcc structure is 4r/ $\sqrt{3}$ . A)3.06 g cm^-3 B)12.2 g cm^-3 C)6.11 g cm^-3 D)2.77 g cm^-3 E)8.46 g cm^-3

Question

Quizplus · Accepted Answer

The volume of a unit cell in a bcc structure is given by:

V = (4r/√3)^3

V = (64r^3)/(3√3)

The number of atoms in one unit cell in a bcc structure is 2:

Density = (mass of one unit cell)/V

To find the mass of one unit cell, we need to find the mass of 2 atoms of vanadium:

mass of 1 atom of vanadium = atomic mass/ Avogadro's number

= 50.9415 g/mol / 6.022 x 10^23 mol^-1

= 8.46 x 10^-23 g

mass of 2 atoms = 2 x 8.46 x 10^-23 g

= 1.69 x 10^-22 g

Density = (1.69 x 10^-22 g) / (64r^3 / (3√3))

= (1.69 x 10^-22 g) / (83.74r^3)

= 2.02 x 10^3 g/cm^3

Substituting the given atomic radius of vanadium, we get:

Density = 6.11 g/cm^3

Therefore, the correct answer is option C.

Vanadium Crystallizes in a Body-Centred Cubic Structure and Has an Atomic