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Calculate the density of silver which cr...

Calculate the density of silver which crystallises in face-centred cubic from. The distance between nearest metal atoms is 287 pm (Molar mass of Ag = `107.87gmol^(-1),(N_(0)=6.022xx10^(23)mol^(-1))`.

Text Solution

Verified by Experts

Density of unit cell `(rho)=(ZxxM)/(N_(0)xxa^(3)xx10^(-30))`
According to available data,
Distance between nearest metal atoms (2r) = 287 pm
Edge length foir fcc crystal (a) `=sqrt2xx2r=sqrt2xx287=405.87"pm"=405.87`
No. of atoms per unit cell (Z) = 4
Atomic mass of silver (M) = `107.87"g mol"^(-1)`
Avogadro's number `(N_(0))=6.022xx10^(23)mol^(-1)`
`"Density of silver"(rho)=(4xx(107.87"g mol"^(-1)))/((405.87)^(3)xx(6.022xx10^(23)"mol"^(-1))xx(10^(-30)"cm"^(3)))="10.72 g cm"^(-3)`
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