Question

Barium crystallizes in a body-centered cubic system with atoms at all lattice points and an edge length of 5.02 angstroms. Calculate its density in g/cm3.

Answer 1

Answer : The density is,
`3.60g/cm^(3)`

Explanation :

Formula used :

`\rho=(Z* M)/(N_(A)* a^(3))` .............(1)

where,

`\rho` = density = ?

Z = number of atom in unit cell (for BCC = 2)

M = atomic mass of barium = 137.3 g/mole

`(N_(A))` = Avogadro's number =
`6.022* 10^(23) mol^(-1)`

a = edge length of unit cell =
`5.02\AA=5.02* 10^(-8)cm`

Conversion used :
`(1\AA=10^(-8)cm)`

Now put all the values in above formula (1), we get

`\rho=(2* (137.3g/mol))/((6.022* 10^(23)mol^(-1)) * (5.02* 10^(-8)cm)^3)=3.60g/cm^(3)`

Thus, the density is,
`3.60g/cm^(3)`