Home
Class 12
CHEMISTRY
If the radius of the octaheral void is r...

If the radius of the octaheral void is `r` and the radius of the atoms in close-packing is `R`, derive relation between `r` and `R`

Text Solution

Verified by Experts

Consider an octahedral void represented by the shaded portion `(` the shown`)`. Now suppose the length of the each arm of the square will be `2R(R` is radius of atom `)`. Let `r` be the radius of void. For right angle triangle `ABC`.
`AC=sqrt([(AB)^(2)+(BC)^(2)])`
`sqrt([(2R)^(2)+(2R)^(2)])=sqrt(8R)`
Also, `AC=R+R+2r=2r+2R=2(r+R)`
or `sqrt(8R)=2sqrt(2R)=2(r+R)`
or `r=sqrt(2R)-R`
`r=[sqrt(2)-1]R=0.414xxR`
Promotional Banner

Topper's Solved these Questions

  • SOLID STATE

    P BAHADUR|Exercise Exercise 9|1 Videos

  • MOCK TEST PAPER

    P BAHADUR|Exercise Exercise|92 Videos

  • SURFACE CHEMISTRY

    P BAHADUR|Exercise Exercise 5|1 Videos

Similar Questions

Explore conceptually related problems

(a) If the radius of octahedral void is r and the radius of the atoms in the close packing is R, derive a relationship between r and R. (b) What is a semiconductor? Describe the two main types of semiconductors and conductor and contrast conduction mechanism in them.

(a) If the radius of octahedral void is 'r' and the radius of the atoms in close packing is 'R' what is the relation between 'r' and 'R' ? (b) A metal crystallises in body centred cubic structure. If 'a' is the edge length of its unit cell, 'r' is the radius of the sphere, what is the relation between 'r' and 'a' ?

If r is the radius of the octahedral voids and R is the radius of the atom in close packing,then :

If the radius of the octahedral void is r and radius of the atom in closet packed structure is R then

If R is the radius of the octahedral voids and r is the radius of the atom in close packing, then r//R is equal to

If radius of an octahedral void is r and atomic radius of atoms assuming cubical close pacting is R. Then the relation between r and R is