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Potassium has a bcc structure with nearest neighbour distance $4.52A^{\large\circ}$.Its atomic weight is 39.Calculate its density.

$\begin{array}{1 1}910kg m^{-3}\\810kg m^{-3}\\710kg m^{-3}\\510kg m^{-3}\end{array} $

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For bcc,$d=\large\frac{\sqrt 3 a}{2}$
Or $a=\large\frac{2d}{\sqrt 3}$
$\Rightarrow \large\frac{2\times 4.52}{1.732}$
$\Rightarrow 5.219A^{\large\circ}$=522pm
$\rho =\large\frac{z\times M}{a^3\times N_A \times 10^{-30}}$
$\Rightarrow \large\frac{2\times 39}{(522)^3\times 6.023\times 10^{23}\times 10^{-30}}$
$\Rightarrow 0.91g/cm^3$
$\Rightarrow 910kg m^{-3}$
answered Aug 4, 2014 by sreemathi.v

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