Ncert Exercises & Solutions

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 cm³ of aluminium?

(i) For a cubic close-packed structure:

a = 2 \sqrt{2} r

= 2 \sqrt{2} \times 125 pm

= 353.55 pm

= 354 pm (approximately)

(ii) Volume of one unit cell = (354 pm)³

= 4.4 \times 10^{7} {pm}^{3}

= 4.4 \times 10^{7} \times 10^{- 30} {cm}^{3}

= 4.4 \times 10^{- 23} {cm}^{3}

Therefore, the number of unit cells in 1.00 cm³

= \frac{1.00 {cm}^{3}}{4.4 \times 10^{- 23} {cm}^{3}} = 2.27 \times 10^{22}