Question

An element with molar mass 64 gmol -1 and density 6.6 g cm -3 forms a cubic unit cell.The edge length of unit cell is 4 x 10 -8cm.The type of cubic unit cell formed is​

Answer 1

Given : An element with molar mass 64g/mol and density 6.6g/cm³ forms a cubic unit cell. The edge length of unit cell is 4 × 10^-8 cm.

To find : The type of cubic unit cell formed is...

solution : using formula,

density of unit cell, d = ZM/a³N

where Z is no of atoms per unit cell,

M is molar mass of element.

a is edge length of unit cell

and N is Avogadro's number.

now, 6.6 g/cm³ = {Z × (64 g/mol)}/{(4 × 10^-8 cm)³ × 6.023 × 10²³ }

⇒6.6 = {Z × 64}/{64 × 10¯²⁴ × 6.023 × 10²³}

⇒6.6 = Z/6.023 × 10¯¹

⇒Z = 6.6 × 6.023 × 10¯¹ = 3.975 ≈ 4

Therefore the no of atoms per unit cell is 4 it means face centered cubic unit cell. ( because it has Z = 4).

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