Question

Barium metal has a body-centered cubic lattice with all atoms at lattice points; its density is 3.51 g/cm3. From these data and the atomic weight, calculate the edge length of a unit cell.

Answer 1

Answer:

The unit cell's edge length is $5.06\times 10^{-8} m$

Explanation:

Number of atom in BCC unit cell = Z = 2

Density of barium metal= $3.51g/cm^3$

Edge length of cubic unit cell= a  = ?

Atomic mass of Ba(M) = 137.33 g/mol

Formula used :  

$\rho=\frac{Z\times M}{N_{A}\times a^{3}}$

where,

= density

Z = number of atom in unit cell

M = atomic mass

$(N_{A})$ = Avogadro's number  

a = edge length of unit cell

On substituting all the given values , we will get the value of 'a'.

$3.51 g/cm3=\frac{2\times 137.33g/mol}{6.022\times 10^{23} mol^{-1}\times (a)^{3}}$

$a = 5.06\times 10^{-8} m$

The unit cell's edge length is $5.06\times 10^{-8} m$