Q. 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 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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A

4

B

2

C

3

D

5

Solution:

$d=\frac{Z \times M}{a^{3} \times N_{A}}$
$M=\frac{\left(\right. 400 \left(\left.\right)^{3} \times 1 0^{- 30} \times 8 \times N_{A}}{4}$
On solving $M=64\times 2\times 10^{- 24}$ $N_{A}g$
Now, $\left(\right.64\times 2\times 10^{- 24}N_{A}\left.\right)$ g contains $N_{A}$ atoms
As $256$ g $=\frac{N_{A}}{64 \times 2 \times 1 0^{- 24} N_{A}}\times 256$
$=2\times 10^{24}$

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