Potassium crystallizes in bcc unit cell with distance nearest neighbours of 4.52 Å, if its atomic mass = 39 amu.
(a)What would be edge length of unit cell ?
(b)What would be the density of K metal ?
(c ) How many nearest neighbouring atoms does each potassium atom has ?

Explanation

(a) The distance between nearest neighbours
`=(1)/(2)xx` length of the body diagonal `= (1)/(2)xx sqrt(3)a`
`= (1)/(2)xx sqrt(3)xx 5.20 Å 4.50 Å`.
(b) Distance between the next nearest neighbours
`a = 5.20 Å`
(c ) Number of K atoms (nearest neighbours) present at a distance of `sqrt(3)a//2` from the body centred atom = 8
(d) Number of K atoms (next nearest neighbours) present at distance of edge length = 6.
(e ) Density `= (n xx M_(m))/(N_(o)xx a^(3))`
where n = number of atoms in one unit cell of bcc = 2
`M_(m) =` Molar mass of K
`= (2xx39)/(6.023xx10^(23)xx(5.20xx10^(-8))^(3))=0.921 gm//cm^(3)`.