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 cm^{3} of Al?

#### Solution

**Given:** Type of unit cell is ccp.

Edge length (a) = 353.6 pm = 3.536 × 10^{–8} cm Volume (V) of Al = 1.00 cm^{3}

**To find:**

1. Radius of Al atom (r)

2. Number of unit cells in 1.00 cm^{3} 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 cm^{3} 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 × 10 ^{22}**.