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Calculate the packing efficiency in simple cubic unit cell. |
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Answer» SOLUTION :In a simple cubic UNIT cell, two spheres at the corners of the cube touch each other. Let edge length of cube = a. Let radius of SPHERE = R The radius of sphere and edge length of cube is related as: a = 2r The volume of cubic unit cell `= a^3 = (2r)^3 = 8r^3` Since the simple cubic unit cell contains only 1 atom, the volume of the occupied space is= `4/3 pi r^3` % Packing efficiency =`("Volume occupied by four spheres in unit cell" xx 100)/("Volume of the unit cell")` ` = 4/3 pi r^3_(8 r^3) xx 100 = pi/6 xx 100` `52.4%`. |
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