1.

An element with molar mass 2.7 xx 10^(-2) kg mol^(-1) forms a cubic unit cell with edge length 405 pm. If its density is 2.7 xx 10^(3) kg m^(-3), what is the nature of the cubic unit cell ?

Answer»

SOLUTION :Applying the FOLLOWING relation, we have
`"Density "=(zxxM)/(a^(3)N_(A)) or Z=("Density"xxa^(3)xxN_(A))/(M)"….(i)"`
`M=2.7xx10^(-2)" kg mol"^(-1), a="405 pm "=405xx10^(-12)m=4.05xx10^(-10)m`
`"Density "=2.7xx10^(3)" kg m"^(-3)`
Thus, all the values of are in SI units.
Substituting the values in equation (i) above, we have
`z=(2.7xx10^(3)xx4.05^(3)xx10^(-30)xx6.022xx10^(23))/(2.7xx10^(-2)) or z=4`
As there is 4 atoms in a unit cell, it is a face-centred CUBIC.


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