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/ . 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

First, we need to calculate the volume of the unit cell:
V = (4r/√3)^3 = (4(131 pm)/√3)^3 = 3.402 x 10^-22 cm^3

Next, we need to calculate the mass of one unit cell, which is the atomic weight of vanadium (50.94 g/mol) divided by Avogadro's number (6.022 x 10^23):
m = 50.94 g/mol / 6.022 x 10^23 = 8.478 x 10^-23 g

Finally, we can calculate the density:
density = mass/volume = 8.478 x 10^-23 g / 3.402 x 10^-22 cm^3 = 2.49 g/cm^3

The closest choice is C (6.11 g/cm^3).

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