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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.

Text Solution

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The molecular mass 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))rArrM=(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)`
47.59 g 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)/(47.59"g mol"^(-1))`
= `12.656xx10^(23)` atoms
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