Question

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 1

Dear Student,

● Answer -

a = 353.6×10⁻¹⁰ cm

N = 2.262×10²² unit cells

◆ Explaination -

# Given -

r = 125 pm

V = 1 cm³

# Solution -

(i) In CCP structure,

a = 2√2 r

a = 2√2 × 125

a = 353.6 pm

a = 353.6×10⁻¹⁰ cm

(ii) No of unit cells in 1 cm³ is given by -

N = V / a³

N = 1 / (353.6×10⁻¹⁰)³

N = 2.262×10²² unit cells

Therefore, length of side of unit cell is 353.6 pm and 1 cm³ of alumnium contain 2.262×10²² unit cells.

Hope this helps ...