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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? - Chemistry

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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/cm3

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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