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An element with molar mass 27 g mol−1 forms a cubic unit cell with edge length 4.05 ✕ 10−8 cm. If its density is 2.7 g cm−3, what is the nature of the cubic unit cell? - Chemistry

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An element with molar mass 27 g mol−1 forms a cubic unit cell with edge length 4.05 ✕ 10−8 cm. If its density is 2.7 g cm−3, what is the nature of the cubic unit cell?

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Solution

Molar mass of the given element, M = 27 g mol−1 = 0.027 kg mol−1

Edge length, a = 4.05 × 10−8 cm = 4.05 × 10−10 m

Density, d = 2.7 g cm−3 = 2.7 × 103 kg m−3

Applying the relation,

`d=(ZxxM)/(a^3xxN_A)`

Where, Z is the number of atoms in the unit cell and NA is the Avogadro number.

Thus,

`Z=(`

   `=(2.7xx10^3xx(4.05xx10^(-10^3))xx6.022xx10^23)/0.027`

    = 4

Since the number of atoms in the unit cell is four, the given cubic unit cell has a face-centred cubic (fcc) or cubic-closed packed (ccp) structure.

Concept: Number of Atoms in a Unit Cell
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