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Solid State — Chemistry STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceChemistrySolid State4 Marks
Question
An element with molar mass $27\ g/mol$ forms cubic unit cell with edge length of 405 pm. If density of the element is $2.7\ g/cm^3$, what is the nature of cubic unit cell ? (fcc or ccp)
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Answer

Given : Molar mass $= M =27 g mol ^{-1}$
Nature of crystal = cubic unit cell
Edge length $= a =405 pm =4.05 \times 10^{-8} cm$
Density $=\rho=2.7 g cm ^{-3}$
Nature of unit cell $=$ ?
$ \rho=\frac{n \times M}{a^3 \times N_{ A }}$
$\therefore  n=\frac{\rho \times a^3 \times N_{ A }}{M} \text { MaharashtraBoardSolutions.Guru }$
$ =\frac{2.7 \times\left(4.05 \times 10^{-8}\right)^3 \times 6.022 \times 10^{23}}{27}$
$=  3.997$
$\cong  4$
Hence the nature of unit cell = face-centred cubic unit cell
Radius of $Al$ atom $=125 pm$
The nature of cubic unit cell is fcc.

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