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The packing efficiency of the two dimensional square unit cell show in the adjoining fig ,. Is (##PR_CHE_V01_XII_C01_E20_009_Q01.png" width="80%"> |
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Answer» 0.3927 Area occupied by circles ` (" within the square")/("Area of the square") ` ` ( 2 xx pir^(2))/a^(2) ` AC = `SQRT(AB^(2) + BC^(2)) = sqrt(a^(2) + a^(2)) = sqr2 a ` but AC = 4 r( r= radius of each sphere) ` sqrt2 a= 4R or a = 4/sqrt2 r = 2 sqrt2r` packing fraction ` ( 2XX pi r^(2))/((2 sqrt2 r)^(2))= pi/4 = ( 3.143)/4 = 0.785i.e, 78.5%` |
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