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Question
Aluminium crystallises in a cubic close-packed structure. Its metallic radius is 125 pm.
- What is the length of the side of the unit cell?
- How many unit cells are there in 1.00 cm3 of aluminium?
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Solution
i. For cubic close-packed structure:
`r = a/(2 sqrt 2)`
`a = 2 sqrt 2 r`
= `2 sqrt 2 xx 125`
= `2 xx 1.414 xx 125`
= 353.55 pm
= 353.55 × 10−10 cm
= 3.54 × 10−8 cm
ii. Volume of one unit cell = a3
= (3.54 × 10−10)3 cm3
= (44.3 × 10−24) cm3
= 4.43 × 10−23 cm3
Hence, number of unit cells in 1.00 cm3
= `1.00/(4.43 xx 10^-23)`
= `1.00/4.43 xx 10^23`
= 0.225 × 1023
= 2.25 × 1022
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