Aluminium crystallises in a cubic close-packed structure. Its metallic

1.	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?
Answer» Given: Unit cell is cubic close-packed structure. Metallic radius (r) of aluminium = 125 pm. To find: i. The edge length (a) . ii. Number of unit cells in 1.00 cm3 of aluminium. Formulae: i. a =\(\sqrt{8}\)r = 2 \(\sqrt{2}\)r ii. Volume of the unit cell = a³ Calculation: i. For cubic close packing, a = 2\(\sqrt{2}\) r = 2\(\sqrt{2}\)×125 = 353.5 pm = 353.5×10^-10 cm ii. Volume of the unit cell = a³ = (353.5×10^-10)³ = 4.4174×10^-23 Number of unit cells in 1.00 cm3 of aluminium =\(\frac{1.00}{4.4174\times10^{-23}}=2.2638\times10^{22}\) Ans: i. The length of the side of the unit cell = 353.5×10^-10 cm. ii. Number of unit cells in 1.00 cm3 of aluminium = 2.2638×10²².

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?

Answer»

Given: Unit cell is cubic close-packed structure.

Metallic radius (r) of aluminium = 125 pm.

To find:

i. The edge length (a) .

ii. Number of unit cells in 1.00 cm3 of aluminium.

Formulae:

i. a =\(\sqrt{8}\)r = 2 \(\sqrt{2}\)r

ii. Volume of the unit cell = a³

Calculation:

i. For cubic close packing, a = 2\(\sqrt{2}\) r

= 2\(\sqrt{2}\)×125 = 353.5 pm = 353.5×10^-10 cm

ii. Volume of the unit cell = a³ = (353.5×10^-10)³ = 4.4174×10^-23

Number of unit cells in 1.00 cm3 of aluminium =\(\frac{1.00}{4.4174\times10^{-23}}=2.2638\times10^{22}\)

Ans: i. The length of the side of the unit cell = 353.5×10^-10 cm.

ii. Number of unit cells in 1.00 cm3 of aluminium = 2.2638×10²².

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