Aluminium crystallises in a cubic closepacked 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 cm3 of aluminium?

Given, Aluminium crystallises in a cubic close-packed structure.

Its metallic radius is 125 pm.

(i) Length of the side of unit cell for cubic structure = a = 22r

a = 2√2 x 125

a = 354 pm

(ii) Number of unit cells in 1.00 cm3 of aluminium = ?

Volume = a3 = (354 pm)3 = 4.4 x 10-23 cm3    (Since, 1 pm = 10-10)

Number of unit cells in 1.00 cm3 = (1.00 cm3)/(4.4 x 10-23 cm3 )

= 2.27 x 1022

 

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