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The density of a face centred cubic elem...

The density of a face centred cubic element (atomic mass = 40 ) is 4.25 gm `cm^(-3)`, calculate the edge length of the unit cell.

Text Solution

Verified by Experts

The correct Answer is:
400 pm
`"Density"(rho)=(zxxM)/(a^(3)xxN_(0)xx10^(-30))or a^(3)=(zxxM)/(rhoxxN_(0)xx10)`
Atomic mass of element (M) = 60.2 amu = 60.2 g `mol^(-1)` , No. pf atoms per unit cell (z) = 4 Density of the element `(rho)=6.25 g cm^(-3)` , Avogadro's number `N_(0)=6.022xx10^(23)"mol"^(-1)`
`a^(3)=(4xx(60.2"g mol"^(-1)))/((6.25"g cm"^(-3))xx(6.022xx10^(23)"mol"^(-1)))=64xx10^(-24)cm^(3)`
`a= (64xx10^(-24)cm^(3))=4xx10^(-8)cm=400xx10^(-10)cm="400 pm."`
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