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/ .

Answer 1

r = 131 pm ,

for bcc lattice sqrt(3) x a = 4r , ( i.e along body diagonal )

a = 4r/1.732 =2.31 r = 2.31 x131 pm = 302.61 pm

density = z x M/(N x a^3) where z = 2 ( number of atoms per unit cell for bcc),

M = 50.94 for vanadium, N = 6.023 x10^ 23, a = 2.31

d = ( 2 x50.94)/(6.023 x10^ 23 x (302.61)^3 x (10^ -10)^3)

= 6.104 gm/cc