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
Answers
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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