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Question
Aluminium crystallizes in a cubic close-packed structure with a unit cell edge length of 353.6 pm. What is the radius of Al atom? How many unit cells are there in 1.00 cm3 of Al?
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Solution
Given: Type of unit cell is ccp.
Edge length (a) = 353.6 pm = 3.536 × 10–8 cm Volume (V) of Al = 1.00 cm3
To find:
1. Radius of Al atom (r)
2. Number of unit cells in 1.00 cm3 of Al
Formulae:
1. For ccp (fcc) unit cell, r = 0.3535 a
2. Number of unit cells in volume (V) of metal = `"V"/"a"^3`
Calculation:
1. Using formula (i),
r = 0.3535 a
∴ r = 0.3535 × 353.6 = 125 pm
2. Using formula (ii),
Number of unit cells in volume (V) of metal = `"V"/"a"^3`
∴ Number of unit cells in 1.00 cm3 of Al = `(1.00)/(3.536 xx 10^-8)^3 = 2.26 xx 10^22`
1. Radius of Al atom (r) is 125 pm.
2. Number of unit cells in 1.00 cm3 of Al is 2.26 × 1022.
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