NCERT Class XII Chemistry
Chapter - The Solid State
Questions with Solutions

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Question : 44
Total: 50
An element with molar mass 2.7×102 kg mol1 forms a cubic unit cell with edge length 405 pm. If its density is 2.7×103 kg m3, what is the nature of the cubic unit cell?
Solution:  
Given M (molar mass of the element) =2.7×102 kg mol1
a (edge length) = 405 pm =405×1012 m =4.05×1010 m
d (density) =2.7×103 kg m3
NA (Avogadro’s number) =6.022×1023 mol1
Using formula,
Density (d) =
Z×M
a3×NA
or, Z=
d×a3×NA
M

or, Z =
(2.7×103)(4.05×1010)3(6.022×1023)
2.7×102
=4
Number of atoms of the element present per unit cell = 4. Hence, the cubic unit cell must be face-centred or cubic close packed (ccp).
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