question : An element with molar mass 2.7×10-2 kg mol-1 forms a cubic unit cell with edge length 405 pm. If its density is 2.7×103 kg m-3, what is the nature of the cubic unit cell ?

Key points to answer this question :

First of all we need to calculate the number of atoms present in the unit cell (Z) =

Then find the type of the cubic unit cell on the based of number of Z , as follows –

If Z = 1 then This will simple cell (SC)

If Z = 2 then This will Body-centered cubic (BCC)

If Z = 4  then This will be Face-centred Cubic Unit Cell  (FCC)

solution : given data –

Molar mass of the given element , M = 2.7×10-2 kg mol-1

Edge length of given cubic unit cell , a = 405 pm

Density of given cubic unit cell , d = 2.7×103 kg m-3
also we know that avogadro’s number NA = 6.02214076 × 1023 Mol-1
now put all the values in our formula to calculate the value of Z =
SO we find Z = 4 , it means there are four atoms per unit cell and also we have discussed here above that if Z = 4 means the cubic cell is FCC (face centred cubic unit cell ).
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