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NCERT Class XII Chemistry
Chapter - The Solid State
Questions with Solutions

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Question : 24 of 50
Marks: +1, -0
Aluminium crystallises in a cubic close packed structure. Its metallic radius is 125 pm.
(i) What is the length of the side of the unit cell?
(ii) How many unit cells are there in 1.00 cm3^{3} of aluminium?
Solution:  
Given r=125 pm,a=?,r=125\,\text{pm}, a=?, structure =ccp(fcc)=\text{ccp}(\text{fcc})
(i) For ccp(fcc),a=22r\text{(i) For ccp}(fcc), a=2\sqrt{2} r
=2×1.414×125 pm=354 pm=2\times 1.414\times 125\,\text{pm}=354\,\text{pm}
=2×1.414×125 pm=354 pm (ii)=2\times 1.414\times 125\,\text{pm}=354\,\text{pm}\text{ (ii)}
Volume of one unit cell=a3\text{Volume of one unit cell} = a^{3}
=(354×10−10 cm)3=4.44×10−23 cm3= (354\times 10^{-10}\,\text{cm})^{3}=4.44\times 10^{-23}\,\text{cm}^{3}
Number of unit cells in 1 cm3=1 cm34.44×10−23 cm31\,\text{cm}^{3} = \frac{1\,\text{cm}^{3}}{4.44\times 10^{-23}\,\text{cm}^{3}}
=2.25×1022=2.25\times 10^{22}
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