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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 `2.7 xx 10^(3) kg^(-3)`, what is the nature of the cubic unit cell?

Text Solution

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Molar mass of the given element, M =` 27"g ""mol"^-1=0.027"kg ""mol"^-1`
Edge length, a=`4.05xx10^-8"cm"=4.05xx10^10"m"`
Density ,`"d"=2.7"g"cm^-3=2.7xx10^-3"kg ""m^3"`
We know that `"d"=frac{"Z"xx"M"}{a^3xx"N"_"A"}`
Where, `"Z"` is the number of atoms in the unit cell and `"N"_"A"` is the Avogadro number.
Thus,`"Z"=frac{"d"xxa^3xxN_A}{"M"}`
`"Z"=frac{2.7xx10^3(4.05x10^-10)^3xx6.022xx10^23}{0.027}`
`"N"_"A"=6.022xx10^23`
`"Z"=4" or ""z"~=4("fcc")`
Since, the number of atoms in the unit cell is 4, the given cubic unit cell has face-centred cubic (fcc) or cubic-close packed (ccp) structure.
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