Solid vanadium crystallizes in a body-centered cubic structure and has a density of 6.00 g/cm3. First determine the number of atoms of vanadium in a unit cell. Then, calculate the atomic radius of vanadium.

The given question is incomplete. The complete question is as follows.

Solid vanadium crystallizes in a body-centered cubic structure and has a density of 6.00 g/cm3. Assuming the vanadium atomic radius is 132 pm, is the vanadium unit cell primitive cubic, body centered cubic, or face centered cubic.

Explanation:

The given data is as follows.

            Density = 6.00

              radius = 132 pm

Relation between edge length and volume is as follows.

             a = ∛V

                = ∛No. of atoms

                =

                =

                = 2.4 ∛No. of atoms

So, there will be three possibilities which are as follows.

Here, a = 2.4, and r = 1.2 which is not right.

So,         a =

                = 3.02 and, r = 1.31 which is a good fit to the measured radius.

So,       a =

              = 3.81 and r = 1.35 which will not fit to the measured radius as well as BCC.

the positions which points up in upward carbon and down in downward carbon are axial

and vice versa holds true for equatorial positions

so the correct answer with labelled diagram will be

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