An element with molar mass 2.7 × 10^-2 kg/mol forms a cubic unit cell with edge length 405 pm.

Question

An element with molar mass 2.7 × 10^-2 kg mol^-1 forms a cubic unit cell with edge length 405 pm. If its density is 2.7 × 10³ kg m⁻³, what is the nature of the cubic unit cell?

Answer 1

It is given that density of the element, d = 2.7 × 10³ kg m⁻³ 

Molar mass, M = 2.7 × 10⁻² kg mol⁻¹
Edge length, a = 405 pm = 405 × 10⁻¹² m
= 4.05 × 10⁻¹⁰ m
It is known that, Avogadro’s number, NA = 6.022 × 10²³ mol⁻¹ 

Applying the relation,

This implies that four atoms of the element are present per unit cell. Hence, the unit cell is face-centred cubic (fcc) or cubic close-packed (ccp).