JEE Advanced 2017 · Paper 1 · Chemistry Q8

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ChemistryInteger+3Question 26 of 54

A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400 pm. If the density of the substance in the crystal is $8\ \mathrm{g\,cm^{-3}}$ , then the number of atoms present in 256 g of the crystal is $N \times 10^{24}$ . The value of $N$ is

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Answer and worked solution

Official answer: 2

One unit cell. $a=400$ pm $=4\times10^{-8}$ cm, so $a^3=6.4\times10^{-23}\ \mathrm{cm^3}$ . Its mass is
$8\times6.4\times10^{-23}=5.12\times10^{-22}\text{ g},$
and it contains 4 atoms (fcc).

Atoms in 256 g.
$\frac{256}{5.12\times10^{-22}}\times4=2\times10^{24}.$

Answer: 2

Topics:Density of crystals Crystal lattices and unit cells

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