An element with density 10 g cm^{−3} forms a cubic unit cell with edge length of 3 × 10^{−8} cm. What is the nature of the cubic unit cell if the atomic mass of the element is 81 g mol^{−1}?

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#### Solution

Given:

Density (D) = 10 g/cm^{3}

Edge length (a) = 3 x 10^{−8} cm

Atomic mass = 81 g/mol

Formula:

`10=(Zxx81)/((3xx10)^3xx6.022xx10^23)`

`Z=(10xx(3xx10)^3xx6.022xx10^23)/81=2.0073`

∴ Z = 2

The unit cell contains 2 atoms, so it is a body-centred cubic unit cell.

Concept: Calculations Involving Unit Cell Dimensions

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