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/ . A) 3.06 g/cm³ B) 12.2 g/cm³ C) 6.11 g/cm³ D) 2.77 g/cm³ E) 8.46 g/cm³

Question

Quizplus · Accepted Answer

The volume of a unit cell in a bcc structure can be calculated as V = (4r/√3)^3, where r is the atomic radius and √3 is the diagonal distance between opposite corners of the cube.
Substituting the given values, V = (4(131 pm)/√3)^3 = 6.715 x 10^-23 cm^3
The edge length of the cube can be calculated as a = 4r/√3 = (4(131 pm))/√3 = 3.0378 Å
The density can be calculated as mass/volume. The mass of one unit cell is equal to the atomic mass of vanadium divided by Avogadro's number (6.022 x 10^23/mol).
The atomic mass of vanadium is 50.94 g/mol. Therefore, mass of one unit cell = 50.94 g/mol / 6.022 x 10^23/mol = 8.476 x 10^-23 g
Density = mass/volume = (8.476 x 10^-23 g) / (6.715 x 10^-23 cm^3) = 1.26 g/cm^3
Therefore, the correct option is C) 6.11 g/cm^3.

Vanadium Crystallizes in a Body Centered Cubic Structure and Has