Niobium crystallises in body-centred cubic structure if density is 8.55 `g cm^(-3)`, calculate atomic radius of niobium using its atomic mass 93u.

Explanation

Density, `rho = 8.55 g cm^(-3)`
Atomic mass of niobrium, `Aw = 94.0`
`rho = (Z_(eff) xx Aw)/(a^(3) xx N_(A))` or `a^(3) = (Z_(eff) xx Aw)/(rho xx N_(A))`
Or `a^(3) = (2 xx 94)/(8.55 xx 6.02 xx 10^(23)) = (108)/(51.47) xx 10^(-23)`
`= 3.27 xx 10^(-23) cm^(3)`
Or `a = (3.27 xx 10^(-23))^(1//3) cm`
`= 14.29 cm`