Question

Aluminium crystallizes in a cubic close-packed structure with a 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: Type of unit cell is ccp.
Edge length (a) = 353.6 pm = 3.536 × 10^–8 cm Volume (V) of Al = 1.00 cm³

To find:

1. Radius of Al atom (r)

2. Number of unit cells in 1.00 cm³ of Al

Formulae:

1. For ccp (fcc) unit cell, r = 0.3535 a

2. Number of unit cells in volume (V) of metal = `"V"/"a"^3`

Calculation:

1. Using formula (i),

r = 0.3535 a

∴ r = 0.3535 × 353.6 = 125 pm

2. Using formula (ii),

Number of unit cells in volume (V) of metal = `"V"/"a"^3`

∴  Number of unit cells in 1.00 cm³ of Al = `(1.00)/(3.536 xx 10^-8)^3 = 2.26 xx 10^22`

1. Radius of Al atom (r) is 125 pm.

2. Number of unit cells in 1.00 cm3 of Al is 2.26 × 10²².