Question

Niobium has a density of 8.55 g/cm³, an atomic weight of 93 and crystallises in body-centred cubic structure. Calculate the atomic radius of Niobium.

Answer 1

Given Density = 8.55 gcm^-3

Let the length of the edge = a cm

Number of atoms per unit cell, Z = 2

Atomic mass M = 93 u

From the formula , density = ZxM/a³ x N₀, we get

8.55 = 2 x 93/a³ x 6.022 x 10²³ = 36.12 x 10^-24 cm³

Now edge length,a = (36.12 x 10^-24)1/3 = 3.306 x 10^-8 cm

Now radius in body centered cubic, r = √3/4 a

Putting the value of a, we get .r = 1.431 x 10^-10 m