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An element of density 7.2 g cm^(-3) occu...

An element of density 7.2 g `cm^(-3)` occurs in bcc structure with unit cell edge of 280 pm. Calculate molecular mass of the element and number of atoms present in 100 g of the element.

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The molecular ass of the element using following equation, and from molecular mass determine the number of atoms present in 100 g of the element.
Let M be the molar mass of the element.
Volume of unit cell`=a^(3)=(280xx10^(-10)cm)^(3)=21.95xx10^(-24)cm^(3)`
In a body centred cubic structure, z=2
Density, `(zxxM)/(N_(A)xxa^(3))implies M=(rhoxxN_(A)xxa^(3))/(2)`
`M=(7.2g" "cm^(-3)xx6.023xx10^(23)mol^(-1)xx21.95xx10^(-24)cm^(-3))/(2)=47.59g" "mol^(-1)`
47.59g of the element contain `6.023xx10^(23)` atoms.
Therefore, number of atoms in 100 g of the element`=(6.023xx10^(23)" atoms "mol^(-1)xx100g)/(47.59g" "mol^(-1))`
`=12.656xx10^(23)` atoms
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