An element with density 10 g `cm^(-3)` forms a cubic unit cell with edge length `3xx10^(-8)cm`. What is the nature of the cubic unit cell if the atomic mass of the element is 81 g `mol^(-1)`.

Answer

bcc structure

Explanation

`Z=(rhoxxa^(3)xxNo)/(M)`
Density of unit cell `(rho)=10"g cm"^(-3)`, Molar mass of element (M) = 81 g `mol^(-1)`
Avogadro's No. (No) = `6.022xx10^(23)`, Edge length of the unit cell `=3xx10^(-8)` cm.
`Z=((10"g cm"^(-3))xx(3xx10^(-8)cm)^(3)xx(6.022xx10^(23)))/(("81 g mol"^(-1)))=2.006`
`~~2("bcc structure)"`