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 `bc c` strucutre, nearest neighbour distance `(d)` us related to the edge `(a)` as
`d = (sqrt3)/(2) a`
or `a = (2)/(sqrt3)d = (2)/(1.732) xx 365.9 = 422.5` pm
For `bc c` sturcture, `Z_(eff) = 2`
For sodium, `Aw = 23`
`:. r = (Z_(eff) xx Aw)/(a^(3) xx N_(A) xx 10^(-30))`
`= (2 xx 23)/((422.5)^(3) xx (6.02 x10^(23)) xx 10^(-30))g cm^(-3)`
`= 1.51 g cm^(-3)`