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Calculate the packing fraction of simple cubic arrangement. |
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Answer» Solution :In a SIMPLE cubic arrangement `"PACKING fraction (or) efficiency"=("Total volume occupied by spheres in unit cell")/("volume of the unit cell")xx100` Consider the CUBE with an EDGE length .a. Volume of the cube with edge length a as `=axxaxxa=a^(3)"....(1)"` Let .r. is the radius of the sphere `"From the figure a"=2r rArr r=(a)/(2)` `therefore"volume of the sphere with radius r"=(4)/(3)pir^(3)` `=(4)/(3)pi((a)/(2))^(3)` `=(4)/(3)pi((a^(3))/(8))` `=(pia^(3))/(6)"...(2)"` In a simple cubic arrangement, numer of spheres belongs to a unit cell equal to one. `therefore` Total volume occupied by the spheres in sc unit cell `=1xx((pia^(3))/(6))"...(3)"` Dividing 3 by 1 `"Packing fraction "=((pia^(3))/(6))/(a^(3))xx100=(100pi)/(6)=52.31%` Only `52.31%` of the available volume is occupied by the spheres in simple cubic packing, making in efficient use of available space and hence minimizing the ATTRACTIVE forces. 
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