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Potassium crystallizes in a body centred cubic lattice. What is the approximate number of unit cells in 4.0 g of potassium? Atomic mass of potassium = 39.

$\begin{array}{1 1}(A)\;3.09\times 10^{22}&(B)\;3.09\times 10^{20}\\(C)\;3.09\times 10^{18}&(D)\;3.09\times 10^{-22}\end{array} $

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In bcc unit cell there are 8 atoms at the corners of the cube and one atom at the body centre
$\therefore$ No of atoms per unit =$8\times \large\frac{1}{8}$$+1=2$
No of atoms is 4.0 g of potassium =$\large\frac{4}{39}$$\times 6.023\times 10^{23}$
$\therefore$No of unit cells in 4.0 g potassium =$\large\frac{4}{39}\times\frac{6.023\times 10^{23}}{2}$$=3.09\times 10^{22}$
Hence (A) is the correct answer.
answered May 28, 2014 by sreemathi.v

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