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An element crystallises in a cubic cryst...

An element crystallises in a cubic crystal structure. The edge length of its unit cell is 3.15Å. The atomic mass and the density of the element are 96 amu and `10.2g*cm^(-3)`. Predict the crystal lattice possessed by the element.

Text Solution

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Density of a cubic unit cell, `rho=(ZxxM)/(Nxxa^(3))`
Given: `rho=10.2g*cm^(-3)," "M=96g*mol^(-1)," "a=3.15Å`
`=3.15xx10^(-8)cm`
`therefore" "Z=rhoxx(Nxxa^(3))/M=(10.2xx6.022xx10^(23)xx(3.15xx10^(-8))^(3))/96=2`
Z = 2 means that the unit cell is body-centred cubic unit cell. Hence, the element possesses body-centred cubic crystal.
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