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Question

The fraction of the total volume occupied by the atoms present in the simple cube is:

A
π4
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B
π6
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C
π32
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D
π42
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Solution

The correct option is B π6

Let the edge length of the cube be a and radius of atom be r.

Now, in simple cube, number of atoms present =18×8=1

So, volume occupied =1×43πr3

Now, in simple cube atoms at corners will be touching each other.

a=2rr=a2

Volume of cube =a3

So, fraction of total volume occupied =43πr3a3

=43×π×(a2)3a3

=43×π×12

=π6


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