The CORRECT statement(s) for cubic close pack | vedclass

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(A) The efficiency of atom packing is $74 \%$.$(C)$ The number of octahedral and tetrahedral voids per atom are $1$ and $2$,respectively.$(D)$ The uni

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$B, C, D$

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(A) The efficiency of atom packing is $74 \%$.$(C)$ The number of octahedral and tetrahedral voids per atom are $1$ and $2$,respectively.$(D)$ The unit cell edge length is $2\sqrt{2}$ times the radius of the atom.Solution:In a $ccp$ structure,the coordination number of an atom in the bulk is $12$. However,an atom in the topmost layer has fewer nearest neighbours (typically $9$),making statement $(A)$ incorrect.Packing efficiency $= \frac{	ext{Volume occupied by } 4 	ext{ spheres in the unit cell } 	imes 100}{	ext{Total volume of unit cell}} = 74 \%$. Thus,$(B)$ is correct.In $ccp$,the number of octahedral voids is equal to the number of atoms $(N)$,and the number of tetrahedral voids is $2N$. Thus,the number of octahedral and tetrahedral voids per atom are $1$ and $2$,respectively. Thus,$(C)$ is correct.For $fcc/ccp$ unit cells,the relation between edge length '$a$' and radius '$r$' is $4r = \sqrt{2}a$,which implies $a = 2\sqrt{2}r$. Thus,$(D)$ is correct.Therefore,statements $(B)$,$(C)$,and $(D)$ are correct.

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