Niobium crystallises in body centred cubic structure. If density is 8.55 g cm-3, then the atomic radius of niobium is (atomic mass of niobium = 93u) (AllMS 2018)

Given, 3 density 8.55gcm Atomic mass of niobium = 93 u As we know that, 3 A MZ density ...(i) a N Where, M= atomic mass Z = number of atoms per unit cell a = edge length NA= Avogadro’s number For bcc, Z= 2 Putting the value in equation (i) 3 23 93 2 8.55 a 6.02 10 x x x Or, 3 23 2 a 3.6137 10 cm x Or, 8 a 3.306 10 cm x For body centred cube, radius 3 a 4 Or, 8 bcc 3 r 3.306 10 cm 4 x x Or, 8 bcc 10 r 1.43 10 cm 1.43 10 m 143pm x x