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A crystalline solid of a pure substance ...

A crystalline solid of a pure substance has a face-centred cubic structure with a cell edge of 400 pm. If the density of the substance in the crystal is `8 g cm^(-3)`, then the number of atoms present in 256g of the crystal is `N xx 10^(24)`. The value of `N` is

Text Solution

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`rho=(ZxxM)/(a^(3)xxN_(0))`
`(8g cm^(-3))=(4xx(256 g ml^(-1)))/((400)^(3)xx(Nxx10^(24)" mol"^(-1))xx10^(-30) cm^(3))`
or `(8g cm^(-3))xx(64xx10^(6))(Nxx10^(24)" mol"^(-1))xx(10^(-30) cm^(3))`
`=(4xx256g)`
or `8xx64xxN=4xx256`
`N=(4xx256)/(8xx64)=2`
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