Question

Aluminium crystallizes in cubic close packed structure with unit cell edge length of 353.6 pm. What is the radius of Al atom? How many unit cells are there in 1.00 cm³ of Al?

Answer 1

Given : Structure of Al = Cubic close packed structure = ccp structure

Edge length of unit cell = a = 353.6 pm = 3.536 x 10^-8 cm

r = ?

Number of unit cells in 1.00 cm³ of Al = ? (...V= 1.00 cm³ )

Radius of Al atom = r = $\frac{a}{2\sqrt{2}}=\frac{353.6}{2\sqrt{2}}$ = 125 pm

Ans. Radius of Al atom = 125 pm

Volume of one unit cell = a³ = (3.536 x 10^-8)³ = 4.421 x 10^-23 cm³

Number of unit cells = $\frac{V}{a^3}=\frac{1.00}{4.421\times {10}^{-23}}$

= 2.26 X 10²²

Ans. Number of unit cells = 2.26 x 10²².