Question

Calculate the density of sodium at atmospheric pressure from its unit cell structure. The radius of sodium used was 1.2 a.u.

Answer 1

Answer:- Sodium crystalizes in Body-centered cubic (BCC) at room temperature of atmospheric pressure in normal conditions. In another word, the most stable form of sodium metal at atmospheric pressure is Body-centered cubic or (BCC).

In which all eight corners are occupied by atoms(share their 1/8 part) to each of the unit cells and the body center is occupied by sodium metal atom(share full to the unit cell).

Therefore the number of atoms per unit cell = 1*1+1/8*8 = 2 = Z

The relation between radius(r) of the atom and edge length(a) for (BCC) = a= 4*r/

=> a = 4*1.2/ a.u.= 2.77 a.u.

1 a.u. = 10^-10 m = 10^-8 cm

therefore a = 2.77*10^-8 cm

M = atomic mass of sodium = 22.9897 g/mol

N_a= 6.022*10²³ atoms/ mol

density,d= Z*M/N_a*a³

=> d = (2*22.9897)/(6.022*10²³ *(2.77*10^-8)³)g/cm³

= 45.9794*10/21.254*6.022 g/cm³

= 459.974/127.9915g/cm³

=3.5938 g/cm³