Gold (atomic radius = 0.144 nm) crystallises in a face-centred unit cell.

Question:

Gold (atomic radius = 0.144 nm) crystallises in a face-centred unit cell. What is the length of a side of the cell?

Solution:

For a face-centred unit cell:

$a=2 \sqrt{2} r$

It is given that the atomic radius, r = 0.144 nm

So, $a=2 \sqrt{2} \times 0.144 \mathrm{~nm}$

= 0.407 nm

Hence, length of a side of the cell = 0.407 nm

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