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An element crystallizes in a f.c.c. lattice with a cell edge of 250 pm. Calculate the density if 300 g of this element contains 2 × 10^{24} atoms.

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#### Solution

Given: a = 250 pm = 250 × 10^{−12 }m

z = 4

m = 250 × 10^{-10} cm 2 × 10^{24 }atom weighs = 300g

`m=M/N_A(M" is molar mass")`

`"molar mass, M ="(300xx6.02xx10^23)/(2xx10^24)=90.3" g/mol"`

`"Density, "d=(zM)/(a^3N_A)`

`d=(4xx90.3)/((250)^3xx10^-36xx6.02xx10^23)=38.4" g/cm"^3`

Therefore, the density of the given element is 38.4 g/cm^{3 }

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