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Solid State — Chemistry STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceChemistrySolid State4 Marks
Question
Aluminium crystallizes in cubic close packed structure with unit cell edge length of $353.6\ pm$ . What is the radius of Al atom ? How many unit cells are there in $1.00 cm^3$ of Al ?
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Answer

Given : Structure of AI
= Cubic close packed structure
= ccp structure
Edge length of unit cell $= a =353.6 pm$
$=3.536 \times 10^{-8} cm$
$r =$ ?
Number of unit cells in $1.00 cm^3$ of $AI =$ ?Radius of Al atom $=r=\frac{a}{2 \sqrt{2}}=\frac{353.6}{2 \sqrt{2}}=\frac{353.6}{2 \times 1.414}=125 pm$
Volume of one unit cell $=a^3=\left(3.536 \times 10^{-8}\right)^3=4.421 \times 10^{-23} cm^3$
Number of unit cells $=\frac{1.00}{4.421 \times 10^{-23}}=2.26 \times 10^{22}$
Radius of Al atom $=125 pm$
Number of unit cells $=2.26 \times 10^{22}$

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