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An element crystallises in a f.c.c. latt...

An element crystallises in a f.c.c. lattice with edge length of 400 pm. Calculate the density if 200 g of this element contain `2.5xx10^(24)` atoms.

Text Solution

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Density of unit cell `(rho)=(ZxxM)/(a^(3)xxN_(0)xx10^(-30))`
Edge length (a) = 400 pm = 400
No. of atoms per unit cell (Z) = 4
Atomic mass (M) of the element may be calculated as follows :
`2.5xx10^(24)` atoms of the element are present is 200 g
`6.022xx10^(23)" atoms of the element are present in"=((200g)xx6.022xx10^(23))/((2.5xx10^(24)))=48.2g`
`"Density of unit cell"=(4xx"48.2 g mol"^(-1))/((400)^(3)xx(6.022xx10^(23)"mol"^(-1))xx(10^(-30)"cm"^(3)))`
`="5 g cm"^(-3)`
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