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NCERT Class XII Chemistry
Chapter - The Solid State
Questions with Solutions

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Question : 14
Total: 50
If the radius of the octahedral void is r and radius of the atoms in close- packing is R, derive relation between r and R.
Solution:  
R and r are the radii of the octahedral site and atoms respectively,
then from Pythagoras theorem we get
AC2=AB2+BC2
(2R)2=(R+r)2+(R+r)2
or ‌√2R=R+r
⇒(√2−1)R=r
∴‌ r=0.414R
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