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An element crystallizes in a structure h...

An element crystallizes in a structure having fcc unit cell of edge 300 pm. Calculate its density if 180 g of this element contain `3.708xx10^(24)` atoms.

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`a=200"pm"=200xx10^(-10)"cm"=2xx10^(-8)"cm"`
For fcc unit cell, Z = 4
Mass of sample, m = 200 g
No. of atoms in Sample, `n=24xx10^(23)`
Density, `d=(Zxxm)/(a^(3)xxnxx10^(-30))`
`=(4xx200g)/((2xx10^(-8))^(3)"cm"^(3)xx24xx10^(23))`
`=800/(8xx10^(-24)xx24xx10^(23))"g cm"^(-3)`
`=100/(24)"g cm"^(-3)=41.67"g cm"^(-3)`
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