Question

At room temperature, sodium crystallized in a body`-`centred cubic lattrice with `a=4.24Å`. Calculate theoretical density of sodium `(` at wt. of`Na =23)`.

Answer 1

A body-centred cubic unit cell contains 8 atoms at the 8 corners and 1 in the centre.
Hence,
Total number of atoms in a unit cell `=8xx(1)/(8)+1=2`
Volume of unit cell `=a^(3)=(4.24xx10^(-8))^(3) cm^(3)`
So, Density `=(ZxxM)/(N_(0)xxV)=(2xx23)/((6.023xx10^(23))(2.24xx10^(-8))^(3))`
`=1.002 g cm^(-3)`