If the radius of the octahedral void is r ...

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

Question : 14 of 50

Marks: +1, -0

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

A C^{2}=A B^{2}+B C^{2}

(2R)^{2}=(R+r)^{2}+(R+r)^{2}

\; \sqrt{2} R = R + r

\Rightarrow (\sqrt{2} - 1) R = r

\therefore \; r = 0.414 R

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