1.

Calculate the packing efficiency of a metal crystal for a simple cubic lattice.

Answer»

Solution :Let the side of the cube be a and the radius of each particle be r.

Then`""a=2r`
Volume of the unit cell `=(2r)^(3)=8r^(3)`
Simple CUBIC unit cell contains only 1 atom
Volume of the occupied space `=(4)/(3)pir^(3)`
Volume of the occupied space `=(4)/(3)pir^(3)`
`THEREFORE"Packing efficiency "=("Volume of one atom")/("Volume of cubic unit cell")XX100`
`=((4)/(3)pir^(3))/(8r^(3))xx100=(PI)/(6)xx100=52.4%`


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