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Q)

An element crystallises in a structure having fcc unit cell with edge length of 200pm.Calculate its density .If 200g of this element contains $24\times 10^{23}$ atoms.

$\begin{array}{1 1}41.67gcm^{-3}\\51.67gcm^{-3}\\61.67gcm^{-3}\\31.67gcm^{-3}\end{array} $

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A)
For fcc
$z=4$
$N =24\times 10^{23}$ atoms
$a=200$ pm
$\;\;\;=200\times 10^{-10}$pm
$\;\;\;=2\times 10^{-8}$ cm
$d=\large\frac{z\times M}{a^3\times N}$
$\;\;\;=\large\frac{4\times 200}{8\times 10^{-24}\times 24 \times 10^{23}}$
$\;\;\;=\large\frac{1000}{24}$
$\;\;\;=41.67gcm^{-3}$
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