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Question 24

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 1.00 cm3of aluminium?

Answer

In a cubic close packed structure,the length of the side of unit cell is related to radius by an equation r = a/2√2

Or

a = r x 2√2

Putting the values in the equation,we get

a = 125 x 2 x 1.414 = 353.5 pm

Volume of the unit cell= (353.5 x 10-10)3 = 4.42 x 10-23

Number of unit cells in 1 cm3 = 1 / 4.42 x 10-23 = 2.26 x 1022 unit cells.

 

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