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An element crystallizes into structure w...

An element crystallizes into structure which may be described by a cube type of unit cell having one atom on each corner of the cube and two atoms on one of its diagonals. If the volume of this unit cell is `24 xx 10^(-24) cm^3` and density of the element is 7.2 g `cm^(-3)`, calculate the number of atoms present in 200 g of the element.

Text Solution

Verified by Experts

We know that a simple cubic unit cell has atoms=1
Volume of element= `("Mass of element")/("density of element") = (200g)/(7.2 g cm^(-3))= 27.78 cm^3`
Number of unit cells= `("Volume of element")/("Volume of unit cell")=(27.78 cm^3)/(24xx10^(-24)cm^3)= 1.157 xx 10^(24)`
Number of atoms present in the given unit cell = 1+2 (given) = 3
`:.` Number of atoms present in `1.157 xx 10^(24)` unit cells = `3 xx 1.157 xx 10^(24) = 3.471 xx 10^(24)`
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