Vanadium crystallizes in a body centered 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/ .

Question

Vanadium crystallizes in a body centered 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/  .

Quizplus · Accepted Answer

The formula for density is:
Density = (mass of unit cell)/(volume of unit cell)

First we need to find the volume of the unit cell. The edge length (a) of a body centered cubic structure can be related to the atomic radius (r) by the equation:

a = 4r/√3

Plugging in the values given:

a = 4(131 pm)/√3
a = 287.27 pm = 2.8727 Å (convert to Å for consistency)

The volume of the unit cell (V) can be calculated using the equation:

V = a^3

V = (2.8727 Å)^3 = 23.72 Å^3

Now we need to find the mass of the unit cell. Since we know the atomic radius, we can use the atomic mass of vanadium to find the mass of each atom. The atomic mass of vanadium is 50.94 g/mol or 0.08394 g/u.

There are two atoms in a body-centered cubic unit cell, so the mass of the unit cell is:

mass of unit cell = 2(atomic mass of vanadium)
mass of unit cell = 2(0.08394 g/u)
mass of unit cell = 0.16788 g

Finally, we can use the density formula to find the density:

Density = (mass of unit cell)/(volume of unit cell)
Density = 0.16788 g/23.72 Å^3 = 6.111 g/cm^3 (rounded to three significant figures)

Therefore, the answer is C) 6.11 g/cm3.

Vanadium Crystallizes in a Body Centered Cubic Structure and Has