Advertisements
Advertisements
Questions
If the radius of the octahedral void is r and the radius of the atoms in close packing is R, derive the relation between r and R.
The radius of an octahedral void is r and the radius of the atom is R when these are in close-packing. Derive a relationship between the two.
Advertisements
Solution
A sphere with center O is fitted into the octahedral void as shown in the above figure. It can be observed from the figure that ΔPOQ is right-angled
∠POQ = 90°
Now, applying the Pythagorean theorem, we can write:
PQ2 = PO2 + OQ2
⇒ (2R)2 = (R + r)2 + (R + r)2
⇒ (2R)2 = 2(R + r)2
⇒ 2R2 = (R + r)2
⇒ `sqrt 2R = R + r`
⇒ `r = sqrt 2R - R`
⇒ `r = (sqrt 2 - 1)R`
⇒ `r = (1.414 - 1)R`
⇒ r = 0.414 R
RELATED QUESTIONS
What is the formula of a compound in which the element Y forms hcp lattice and atoms of X occupy 2/3rd of tetrahedral voids?
How many tetrahedral voids can exist per unit cell in a hexagonal close packing sphere?
The unit cell of a substance has cations A+ at the corners of the unit cell and the anions B− at the center. The simplest formula of the substance is ____________.
Total number of voids in 0.5 mole of a compound which forms hexagonal close packed structure is ____________.
A compound is formed by two elements A and B. The element B forms cubic close packing and atoms of A occupy `1/3"rd"` of tetrahedral voids. The formula of this compound is ____________.
The Ca2+ and F– are located in CaF2 crystal, respectively at face centered cubic lattice points and in ____________.
Percentages of free space in cubic close packed structure and in the body-centered packed structure are respectively:
In which of the following crystals alternate tetrahedral voids are occupied?
The number of octahedral voids present in a lattice is A. The number of closed packed articles, the number of tetrahedral voids generated is B the number of closed packed particles:
In the hexagonal close-packed structure of a metallic lattice, the number of nearest neighbours of a metallic atom is ____________.
If Germanium crystallises in the same way as diamond, then which of the following statement is not correct?
In the cubic close packing, the unit cell has ______.
Which of the following is not true about the voids formed in 3 dimensional hexagonal close packed structure?
(i) A tetrahedral void is formed when a sphere of the second layer is present above triangular void in the first layer.
(ii) All the triangular voids are not covered by the spheres of the second layer.
(iii) Tetrahedral voids are formed when the triangular voids in the second layer lie above the triangular voids in the first layer and the triangular shapes of these voids do not overlap.
(iv) Octahedral voids are formed when the triangular voids in the second layer exactly overlap with similar voids in the first layer.
Show that in a cubic close packed structure, eight tetrahedral voids are present per unit cell.
In which of the following structures coordination number for cations and anions in the packed structure will be same?
A compound is formed by two elements A and B. The element B forms a cubic close-packed structure and atoms of A occupy `1/3` of the tetrahedral voids. If the formula of the compound is AxBy then the value x + y is in the option:
