Estimate the averaage atomic mass density of a sodium atom, assuming its size ot be 2.5 Å. Compare it with density of sodium in its crystalline phase `(970 kg m^(-3))`. Are the two denities of the same order of magnitude ? If so, why ?

Explanation

Size of atom `=2.5xx10^(-10)m`
Volume of atom `=(4)/(3)pi r^(3)`
`=(4)/(3)xx3.14xx(2.5xx10^(-10))^(3)`
`=(4)/(3)xx3.14xx15.63xx10^(-30)m^(3)`
Mass of `6.02xx10^(23)` atoms of sodium `=23xx10^(-3)kg`
Mass of 1 atom of sodium `=(23xx10^(-3))/(6.02xx10^(23))kg`
Density `=(M)/(V)`
`=(23xx10^(-3))/(6.02xx10^(23))xx(3)/(4xx3.14xx15.63xx10^(-30))`
`=(69xx10^(4))/(6.02xx4xx3.14xx15.63)kgm^(-3)`
`approx 0.6xx10^(3)kgm^(3)`
The two densities are not of the same order due to interatomic spacing in crystalline phase of sodium.