Sodium has a `bc c` structure with nearest neighbour distance of `365.9` pm. Calculate its density. (Atomic mass of sodium `= 23`)

Explanation

For the bcc structure, edge length is related to nearest neighbour distance (d) as
`d = (sqrt3)/2 a " or " a = (2d)/(sqrt3)`
`:. " " a = (2 xx 365.9)/(1.732) = 422.5 p m = 422.5 xx 10^(-1) cm`
Density , `rho = (Z xx M)/(a^3 xx N_A)`
`Z = 2 ( " for bcc ") , M = 23 g mol^(-1), N_A = 6.02 xx 10^(23)`
`:. rho = (2 xx 23)/((422.5 xx 10^(-10))^(3) xx (6.02 xx 10^(23))) = 1.01 g cm^(-3)`