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Question
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.
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