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Chemistry Question on The solid state

The density and edge length values for a crystalline element with fccfcc lattice are 10 g cm−310 \,g \,cm^{-3} and 400 pm400\, pm , respectively. The number of unit cells in 32 g32 \,g of this crystal is

A

8×10238\times 10^{23}

B

5×10225\times 10^{22}

C

8×10228\times 10^{22}

D

5×10235\times 10^{23}

Answer

5×10225\times 10^{22}

Explanation

Solution

Volume of the unit cell =a3=(400 pm)3=a^{3}=(400\,pm)^{3}
=64×10−30 m3=64×10−24 cm3=64\times 10^{-30}\,m^{3}=64 \times 10^{-24}\,cm^{3}
Density of the unit cell =10 g/cm3=10 \,g/cm^{3}
Mass of unit cell = Volume ×\times density
=64×10−24×10=64 \times 10^{-24}\times10
=640×10−24 g=640 \times 10^{-24}\,g
Now, 640×10−24 g≡1640 \times 10^{-24}\,g \equiv 1 unit cell
∴32 g≡1640×10−24×32\therefore 32\,g \equiv \frac{1}{640 \times 10^{-24}}\times32
=0.05×1024=0.05\times 10^{24}
=5×1022=5\times 10^{22}