Answer :
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 [tex]g/cm^{3}[/tex]
radius = 132 pm
Relation between edge length and volume is as follows.
a = ∛V
= ∛No. of atoms
= [tex]\sqrt[3]{\frac{mass}{density \times N_{A}}}[/tex]
= [tex]\sqrt[3]{\frac{50.941 g/mol}{6.0 g/cm^{3} \times 6.022 \times 10^{23}}}[/tex]
= 2.4 ∛No. of atoms
So, there will be three possibilities which are as follows.
- SC, 1 atom and r = [tex]\frac{a}{2}[/tex]
Here, a = 2.4, and r = 1.2 [tex]A^{o}[/tex] which is not right.
- For BCC, there are two atoms and r = [tex]\frac{\sqrt{3}a}{4}[/tex]
So, a = [tex]1.26 \times 2.4[/tex]
= 3.02 and, r = 1.31 [tex]A^{o}[/tex] which is a good fit to the measured radius.
- For FCC, there are 4 atoms and r = [tex]\frac{\sqrt{2}a}{4}[/tex]
So, a = [tex]1.59 \times 2.4[/tex]
= 3.81 and r = 1.35 [tex]A^{o}[/tex] which will not fit to the measured radius as well as BCC.