Voids

Q.

The distance between an octahedral and tetrahedral void in an fcc lattice is?

1. $\mathrm{a}\surd 3$

2. $\frac{\mathrm{a}\surd 3}{2}$

3. $\frac{\mathrm{a}\surd 3}{4}$

4. $\frac{\mathrm{a}\surd 3}{6}$

Q. A compound with formula $A{B}_2{O}_4$ adopts a crystal structure in which $O^{2-}$ ions forms ccp arrangement. $A^{2+}$ ions occupy octahedral voids while $B^{3+}$ ions are distributed equally between tetrahedral and octahedral voids. The fraction of octahedral and tetrahedral voids occupied respectively are:

1. $12.5\%,50\%$
2. $50\%,12.5\%$
3. $25\%,50\%$
4. $50\%,25\%$

Q.

In a solid, oxide ions (${\mathrm{O}}^{2-}$) are arranged in ccp, cation (${\mathrm{A}}^{3+}$) occupies one-sixth of the tetrahedral void, and cations (${\mathrm{B}}^{3+}$) occupy one-third of the octahedral voids. What is the formula of the compound?

1. ${\mathrm{ABO}}_2$

2. ${\mathrm{ABO}}_3$

3. ${\mathrm{A}}_2{\mathrm{BO}}_3$

4. ${\mathrm{AB}}_2{\mathrm{O}}_3$

Q. Equal volumes of $0.1\text{M}AgN{O}_3$ and $0.2\text{M}NaCl$ are mixed. The concentration of $N{O}_3^{-}$ ions in the mixture will be:

1. $0.1\text{M}$
2. $0.05\text{M}$
3. $0.15\text{M}$
4. $0.20\text{M}$

Q.

In FCC, 50% of tetrahedral voids are filled. Find the effective number of atoms in a unit cell if it consists of the same atoms in the lattice and voids.

1. 6

2. 8

3. 4

4. 5

Q. Stacking of a second layer of sphere over the first layer of 2-D hexagonal close packing will result in formation of:

1. Only octahedral voids
2. Only triangular voids
3. Only tetrahedral voids
4. Both tetrahedral and octahedral voids

Q.

Give the chemical formula and compute the ratio by mass of combining elements in Aluminium fluoride.

Q. An element has face-centred cubic (fcc) structure with a cell edge of a. The distance between the centres of two nearest tetrahedral voids in the lattice is:

1. $\frac{a}{2}$
2. $\frac{\sqrt{3}a}{2}$
3. $a$
4. $2a$

Q.

Ionic radii of $M{g}^{2+}$ and $O^{2-}$ ions are 66 pm and 140 pm respectively. The type of interstitial void and coordination number of $M{g}^{2+}$ ion respectively are

1. tetrahedral, 12

2. Octahedral, 6

3. tetrahedral, 6

4. octahedral, 8

Q. Structure of a mixed oxide is cubic close packed $\left(ccp\right)$. The cubic unit cell of mixed oxide is composed of oxide ions. One fourth of the tetrahedral voids are occupied by divalent metal $A$ and the octahedral voids are occupied by a monovalent metal $B$. The formula of the oxide is:
(AIPMT 2012)

1. $AB{O}_2$
2. $A{B}_2{O}_2$
3. $A_{2}B{O}_2$
4. $A_2{B}_3{O}_4$

Q. A compound with formula $A{B}_2{O}_4$ adopts a crystal structure in which $O^{2-}$ ions forms ccp arrangement. $A^{2+}$ ions occupy octahedral voids while $B^{3+}$ ions are distributed equally between tetrahedral and octahedral voids. The fraction of octahedral and tetrahedral voids occupied respectively are:

1. $12.5\%,50\%$
2. $50\%,12.5\%$
3. $25\%,50\%$
4. $50\%,25\%$

Q. In an oxide, oxide ions are packed in an FCC unit cell in which $B^{3+}$ ions occupy x% of octahedral voids and $A^{2+}$ ions occupy y% of tetrahedral voids, then which of the following is/are correct about the unit cell?

1. Formula is $A_{2}B{O}_8$ in which x= 12.5% and y= 12.5%
2. Formula is $A_2{B}_4{O}_6$ in which x= 50% and y= 50%
3. Formula is $A{B}_2{O}_4$ in which x= 50% and y= 12.5%
4. Formula is $A_{2}B{O}_2$ in which x= 12.5% and y= 50%

Q. Which of the following statements regarding close packing is correct?

Q. Element ‘B’ forms ccp structure and ‘A’ occupies half of the octahedral voids, while oxygen atoms occupy all the tetrahedral voids. The structure of bimetallic oxide is:

1. $A_2{B}_{2}O$
2. $A{B}_2{O}_4$
3. $A_4{B}_{2}O$
4. $A_{2}B{O}_4$

Q. An element crystallises in a face-centred cubic (fcc) unit cell with edge length $a$. The distance between the centres of two nearest octahedral voids in the crystal lattice is:
(JEE Main 2020)

Q.

A crystallises in BCC arrangement and ions B occupy ${\frac{1}{3}}^{rd}$ of tetrahedral voids. What is the formula of the crystal?

1. $A_3{B}_4$

2. $A_3{B}_2$

3. $A_5{B}_2$

4. $A_3{B}_4$

Q. If N is the number of spheres in the unit cell, then total number of octahedral voids is the cell is .

1. 2N
2. 3N
3. N

Q. The density of a pure substance ‘A’, whose atoms are arranged in a cubic close pack arrangement, is $1\text{g/cc}$. If all the tetrahedral voids are now filled with ‘B’ atoms, what is the density of the resulting solid in $\text{g/cc}$? [Molar mass $A=30\text{g/mol}$ and Molar mass $\text{B = 50 g/mol}]$

1. 3.33
2. 4.33
3. 2.33
4. 5.33

Q. A solid is made of two elements X and Z. The atoms Z are in CCP arrangement while the atom X occupy two-third of the tetrahedral sites. What is the formula of the compound?

1. XZ
2. $X{Z}_2$
3. $X_4{Z}_3$
4. $X_2{Z}_3$

Q. A crystal is made up of particles X, Y and Z; X forms FCC packing, Y occupies all the octahedral voids of X and Z occupies all the tetrahedral voids of X. If all the particles along one body diagonal are removed, then the formula of the crystal would be:

1. $XY{Z}_2$
2. $X_{2}Y{Z}_2$
3. $X_8{Y}_4{Z}_5$
4. $X_5{Y}_4{Z}_8$

Q.

In a compound oxide ions are present in CCP. $\frac{1}{6}$ th of the tetrahedral voids are occupied cation A and $\frac{1}{3}$ rd of the octahedral voids are occupied by cation B. What is the formula of the compound and what are the charges on A and B respectively.

1. $A^{5+}{B}^{+}{O}^{3-},AB{O}_3$

2. $A^{5+}{B}^{+}{O}^{3-},A_{2}B{O}_3$

3. $A^{4+}{B}^{2+}{O}^{3-},AB{O}_3$

4. $A^{6+}{B}^{+}{O}^{3-},A{B}_2{O}_3$

Q. A solid is made of two elements X and Z. The atoms Z are in CCP arrangement while the atom X occupy two-third of the tetrahedral sites. What is the formula of the compound?

1. XZ
2. $X{Z}_2$
3. $X_4{Z}_3$
4. $X_2{Z}_3$

Q. Which of the following statement(s) regarding close packing is/are correct?

1. In 1D, efficient packing is when spheres does not touch each other.
2. In 2-D, AAA... type arrangement gives square close packing
3. The coordination number of square close packing in 2-D is 8
4. Particles are assumed as identical sphere in measuring packing efficiency

Q. If N is the number of spheres in the unit cell, then total no. of tetrahedral voids is .

1. 2N
2. 3N
3. 4N

Q.

In a compound, oxide ions constitute cubic close packing. Cations A occupy 50% of tetrahedral holes while cations B occupy all the octahedral voids. The empirical formula of the compound is ?

1. $A{B}_2{O}_4$

2. $AB{O}_2$

3. $A_{2}B{O}_4$

4. $ABO$

Q.

The arrangement of $X^{-}$ ions around $A^{+}$ ion in solid AX is given in the figure (not drawn to scale). If the radius of $X^{-}$ is 250 pm, the ideal radius of $A^{+}$ is

1. 104 pm

2. 183 pm

3. 125 pm

4. 57 pm

Q. Total number of voids in $0.5mol$ of a compound forming hexagonal closed packed structure are

1. $3.011\times {10}^{23}$
2. $9.033\times {10}^{23}$
3. $6.022\times {10}^{23}$
4. $4.516\times {10}^{23}$

Q. A crystal is made up of particles $X,Y$ and $Z$. $X$ forms FCC packing. $Y$ occupies all the octahedral voids of $X$ and $Z$ occupies all the tetrahedral voids of $X$. If all the particles along one body diagonal are removed, then the formula of the crystal would be:

1. $XY{Z}_2$
2. $X_{2}Y{Z}_2$
3. $X_8{Y}_4{Z}_5$
4. $X_5{Y}_4{Z}_8$

Q. An element crystallises in a face-centred cubic (fcc) unit cell with edge length $a$. The distance between the centres of two nearest octahedral voids in the crystal lattice is: