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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

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Verified by Experts

The correct Answer is:
2
We know,
`Z=(a^(3)xxd xx N_(A))/(m)`
Molar mass of solid can be calculated as,
`m=(a^(3)xxd xx N_(A))/(Z)`
`=((400xx10^(-10))^(3)xx8xxN_(A))/(4)`
`=(64xx2xx10^(-24))N_(A)`
Number of atoms `=("Mass")/("Molar mass")xxN_(A)`
`=(256)/((64xx2xx10^(-24)N_(A)))xxN_(A)`
`=2xx10^(24)`
`therefore " "N=2`
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