Potassium crystallizes in body centered cubic lattice with a unit cell length `a = 5.2 Å`
(A) what is the distance betweenn nearest neighbourss?
(B) What is the distance between next nearest neighbour ?
(C) How many nearest neighbours does each K atom have ?
(D) How many next nearest neighbours does each K has ?
(E) What is calculated density of crystalline K

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)`.