1.

Calculatethe percentageefficiencyof packing in case of bodycenteredcubiccrystal.

Answer»

SOLUTION :Packingefficiency: inbodycenteredcubicarrangementthe spheresare touchingalongtheleadingdiagonalof the cubeas shownin the FIGURE.
`AC^(2) - AB^(2) + BC^(2)`
`AC = sqrt(a^(2) +a^(2)) = sqrt(2a^(2))= sqrt(2a)`
In `Delta ACG`
`AG^(2) = AC^(2) +CG^(2)`
`AG = sqrt((2a)^(2) +a^(2))`
i.e., `sqrt(3) a= 4r`
Volumeof THESPHERE withradiusr
Numberof spherebelongto aunitcell inbccarrangement is equalto twoandbencethe totalvolumeof allspheres

Packin fraction= `("Totalvolumeoccupiedbyspheresin a unitcell ") /("Volumeof theunitcell") xx 100`
Packingfraction`=((sqrt(3) pi a^(3))/( 8))/((a^(3))) xx 100`
`=1.732 xx 3.14xx 12.5=68%`


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