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  • Niobium is found to crystallise with bcc structure and found to have density of 8.55 gram per centimetercube.

Niobium is found to crystallise with bcc structure and found to have density of 8.55 gram per centimetercube. Determine the atomic radius of niobium if it's atomic mass is 93??

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It is given that the density of niobium, d = 8.55 g\: cm^{-1}
Atomic mass, M = 93 g\:mol^{-1}
As the lattice is bcc type, the number of atoms per unit cell, z = 2

We also know that, N_A=6.022 \times 10^{23}\: mol^{-1}

\\Apply\:the\:relation,\: d=\frac{zM}{a^3N_A}\\\Rightarrow a^3=\frac{zM}{dN_A}=\frac{2\times93}{8.55\times6.022\times10^{23}}\Rightarrow a=3.306 \times 10^{-8} cm\\For \:body-centred \:cubic\: unit\: cell:\\r=\frac{\sqrt3}{4}a=14.32nm

g mol¯l 6.022 x 1 mol¯l Apply the relation, d 2 x 93 ciNA 8.55 x 6.022 x 1023 For body — centred cubic unit cell • a = 14.32nm 4 3.306 x 10-8 cm
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himanshu.meshram

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