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The fraction of volume occupied by atoms...

The fraction of volume occupied by atoms in a primitive cubic unit cell is nearly:

A

`pi//4`

B

`pi//6`

C

`pi/3sqrt2`

D

pi/4sqrt2`

Text Solution

Verified by Experts

The correct Answer is:
B
In a simple cube, number of atoms/unit cell
`=8times 1/8=1`
`" Volume of the cube"=4//3pir^(3)`
`" Volume of the cube" = a^(3)=(2r)^(3) = 8 r^(3)(therefore a =2r)`
`therefore "Fraction occupied" = (4//3timespir^(3))/(8r^(3)) = pi/6`
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