The crystalline structure of a solid is CCP for ‘X’ atoms. If ‘Y’ atoms occupy all the octahedral vo

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The crystalline structure of a solid is CCP for ‘X’ atoms. If ‘Y’ atoms occupy all the octahedral voids and ‘Z’ atoms occupy all the tetrahedral voids, without any distortion in the CCP arrangement of ‘X’ atoms, then the fraction of body diagonal not covered by the atoms is

Accepted Answer

Fraction of body diagonal covered$= \frac{2r + 2 	imes 0.414r + 4 	imes 0.225r}{\sqrt{3} 	imes \left( \frac{4r}{\sqrt{2}} ight)} = 0.76$∴ Fraction, not covered = 1 – 0.76 = 0.24

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