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Aluminium (atomic mass 27) forms crystals in the cubic crystal system with a unit-cell edge length of 4.05 Å. If its density is 2.7 g cm⁻³, identify the type of unit cell and find the atomic radius of Al.

1. face-centred cubic, 2.432 Å
2. body-centred cubic, 2.432 Å
3. body-centred cubic, 1.432 Å
4. face-centred cubic, 1.432 Å

Correct answer: face-centred cubic, 1.432 Å

Solution

Z = d*Na*a^3/M = 2.7*6.022e23*(4.05e-8)^3/27 = 4, so the cell is face-centred cubic. For FCC, 4r = sqrt2 a gives r = 1.414*4.05/4 = 1.432 A. The stored 'bcc' is wrong.

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