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An element with molar mass 2.7 xx 10^(-2...

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 ?

Text Solution

Verified by Experts

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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