Packing Fraction and Efficiency

Q. Consider the bcc unit cells of the solids $1$ and $2$ with the position of atoms as shown below. The radius of atom $B$ is twice that of atom $A$. The unit cell edge length is $50\%$ more in solid $2$ than in $1$. What is the approximate packing efficiency in solid $2$?

1. $65\%$
2. $90\%$
3. $75\%$
4. $45\%$

Q. The ratio of number of atoms present in a simple cubic, body centered cubic and face centered cubic structure, respectively, are :

1. $8:1:6$
2. $1:2:4$
3. $4:2:1$
4. $4:2:3$

Q. For the given 2-D parallelogram unit cell in hexagonal close packing, the packing fraction will be:

Q.

The total volume of atoms present in an FCC unit cell of a metal radius r is:

1. $\frac{12}{3}{\mathrm{\pi r}}^3$

2. $\frac{20}{3}{\mathrm{\pi r}}^3$

3. $\frac{16}{3}{\mathrm{\pi r}}^3$

4. $\frac{24}{3}{\mathrm{\pi r}}^3$

Q. The silver metal crystallizes with a face-centred cubic lattice. The edge length of the unit cell is $4.08\stackrel{o}{A}$. Calculate the percentage of empty space in the FCC structure?

Q. Which of the following relation is true for cubical voids?
Where, $R$ is radius of sphere
$r$ is radius of cubical void
$a$ is edge length of unit cell

Q.

In which of the following arrangements a metal could have least density?

1. B.C.C

2. C.C.P

3. H.C.P

4. Simple cubic

Q. Calculate the percentage of space occupied by the voids in body centred cubic unit cell.

1. 54%
2. 32%
3. 68%
4. 26%

Q. Which of the following statement(s) is/are incorrect regarding tetrahedral voids in fcc lattice?

1. Each face diagonals contains 2 tetrahedral voids
2. Each body diagonals contains 2 tetrahedral voids.
3. Each tetrahedral void contributes $\frac{1}{4^{th}}$ part to a unit cell
4. One tetrahedral void is present at the body centre of unit cell

Q. Which of the following statement is correct regarding tetrahedral voids in fcc lattice?

1. Each body diagonals contains 2 tetrahedral voids.
2. Each face diagonals contains 2 tetrahedral voids
3. Each tetrahedral void contributes $\frac{1}{4^{th}}$ part to a unit cell
4. One tetrahedral void is present at the body centre of unit cell

Q.

Calculate packing fraction from the following figure to two decimal places. Multiply it by 100 and enter the value.

___

Q. Packing fraction is minimum in .

1. simple cubic
2. face centred cubic
3. body centred cubic

Q.

Calculate the packing efficiency in a body centered cubic (BCC) lattice.

Q. If Z is the number of atoms in the unit cell that represents the closest packing sequence ABCABC....., the number of tetrahedral voids in the unit cell is equal to

Q. Match the following cubic structure with its packing fraction

1. 68%
2. 74%
3. 52.4%
4. 74%

Q. The vacant space in a BCC lattice unit cell is :

1. $23\%$
2. $32\%$
3. $26\%$
4. $48\%$

Q. Which 3-D packing has the maximum empty space in its crystal lattice?

Q. The pyknometric density of sodium chloride crystal is $2.165\times {10}^3$ kg $m^{-3}$ while its X - ray density is $2.178\times {10}^3$ kg $m^{-3}$. The fraction of unoccupied sites in sodium chloride crystal is:-
AIPMT-2003

Q.

Fraction of total volume occupied by atoms in a simple cubic cell is

1. 

2. 

3. 

4. 

Q. A body centered cubic lattice is made up of hollow spheres of B. Spheres of solid A are present in hollow spheres of B. Radius A is half of radius of B. What is the ratio of total volume of spheres of B unoccupied by A in a unit cell and volume of unit cell?

1. $\frac{7\sqrt{3\pi }}{64}$
2. $\frac{7\pi }{24}$
3. $\frac{7\pi \sqrt{3}}{64}$
4. $\frac{7\sqrt{3}}{128}$

Q. Percentage of free space in cubic close packed structure and in body centred cubic structure are respectively:

1. $48\%$ and $26\%$
2. $30\%$ and $26\%$
3. $26\%$ and $32\%$
4. $32\%$ and $48\%$

Q. In a cubic lattice of X and Y, X atoms are present at the corners and body centre while Y atoms are at face centres and edge centres. What would be the simplest formula of the compound be if two corner atoms of X and 4 edge centre atoms of Y are replaced by Z atoms?

1. $X_{20}{Y}_5{Z}_7$
2. $X_7{Y}_{19}{Z}_3$
3. $X_7{Y}_{20}{Z}_5$
4. $X_3{Y}_{19}{Z}_7$

Q. Calculate the percentage of space occupied by the voids in body centred cubic unit cell.

1. 26%
2. 32%
3. 68%
4. 54%

Q. Position of octahedral voids in fcc structure is/are:

1. Corners of unit cell
   
2. Edge centres of unit cell
   
3. Face-centres of unit cell
4. Body centres of unit cell

Q.

Packing fraction is minimum in which of the following?

1. Face Centre Cubic

2. Body Centre Cubic

3. Simple Cubic Close packing

4. Hexagonal Close Packing

Q. Packing fraction in a hexagonal arrangement is:

1. $\frac{\pi }{3\sqrt{2}}$
2. $\frac{\pi }{3\sqrt{3}}$
3. $\frac{\pi }{2\sqrt{3}}$
4. $\frac{\pi }{6}$

Q. A metal crystallizes in a face centered cubic structure. If the edge length of its unit cell is ‘$a$’, the closest approach between two atoms in metallic crystal will be:

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

Q. A metal crystallizes in a face centered cubic structure. If the edge length of its unit cell is ‘$a$’, the closest approach between two atoms in metallic crystal will be:

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

Q.

A metallic element crystallizes into a lattice containing a sequence of layers of ABABAB. . . .Percentage of empty space (by volume) is

1. $52\%$

2. $26\%$

3. $50\%$

4. $74\%$

Q. Select the right expression for determining the Packing fraction (PF) of NaCl unit cell (assume an ideal crystal), if the ions along an edge diagonal are absent: (Where $r_{+}$ represents the radius of the cation and $r_{-}$ represents the radius of the anion)

1. $PF=\frac{d\frac{4}{3}[r_{+}^3+r_{-}^3]}{16\sqrt{2}{r}_{-}^3}$
2. $PF=\frac{\frac{4}{3}\pi [\frac{5}{2}{r}_{+}^3+4r_{-}^3]}{16\sqrt{2}{r}_{-}^3}$
3. $PF=\frac{\frac{4}{3}\pi [\frac{5}{2}{r}_{+}^3+r_{-}^3]}{16\sqrt{2}{r}_{-}^3}$
4. $PF=\frac{\frac{4}{3}\pi [\frac{7}{2}{r}_{+}^3+r_{-}^3]}{16\sqrt{2}{r}_{-}^3}$