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Question
The fraction of total volume occupied by the atoms present in a simple cube is
The fraction of total volume occupied by the atoms present in a simple cube is
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Solution
Let the edge length of cube be a.
Then the volume of total cube is a3.
As in simple cubic cell, the atoms are present only at the corners and touches each other therefore a = 2r
Hence, Volume in terms of radius = (2r)3
= 8r3.
The number of atoms present in simple cube is 1 atom per lattice.
Therefore the volume of one atom whose radius is r = 4/3 π r3.
Hence the fraction of total volume occupied by the atoms present in a simple cube is = 4/3 π r3/ 8r3 × 100 %
= π/6 × 100 %
= 52.4 %.
Let the edge length of cube be a.
Then the volume of total cube is a3.
As in simple cubic cell, the atoms are present only at the corners and touches each other therefore a = 2r
Hence, Volume in terms of radius = (2r)3
= 8r3.
The number of atoms present in simple cube is 1 atom per lattice.
Therefore the volume of one atom whose radius is r = 4/3 π r3.
Hence the fraction of total volume occupied by the atoms present in a simple cube is = 4/3 π r3/ 8r3 × 100 %
= π/6 × 100 %
= 52.4 %.
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