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Aluminium crystallises in a cubic close-...

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 `1.00cm^(3)` of aluminium?

Text Solution

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Cubic close packing (CCP) `-=` FCC
For FCC, `4r = sqrt(2)xx a`
`rArr 2sqrt(2)xx sqrt(2)r = sqrt(2)xx a`
`a = 2sqrt(2)r`
`= 2xx4.414xx125`
= 354 cm.
Volume of unit cell `= (354xx10^(-10)cm)^(3)`
`= 4.4xx10^(-23)cm^(3)`
Unit cell in `1 cm^(3)=(1)/(414xx10^(-23))=2.25xx10^(23)`.
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