Packing Fraction and Efficiency

Q.

Total volume of atoms present in a face centred cubic unit cell of a metal is (r = radius of atom).

1. $\frac{24}{3}\pi r^3$

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

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

4. $\frac{12}{3}\pi r^3$

Q.

Aluminium crystallises in a cubic close-packed structure. Its metallic radius is 125 pm.

(i) What is the length of the side of the unit cell?

(ii) How many unit cells are there in 1.00 cm³ of aluminium?

Q. The coordination number of $Z{n}^{2+}$ and $S^{2-}$ ions in the zinc blende $\left(ZnS\right)$ type structure is

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

Q. At ${100}^{\circ }C,$ copper $\left(Cu\right)$ has fcc unit cell structure with cell edge length of $x\stackrel{\circ }{A}$ . what is the approximate density of Cu $\left(\text{in g}c{m}^{-3}\right)$ at this temperature? [Atomic mass of $Cu$ $=63.55u]$
(JEE Main 2019)

1. $\frac{211}{x^3}$
2. $\frac{105}{x^3}$
3. $\frac{422}{x^3}$
4. $\frac{205}{x^3}$

Q. If the radius of a metal atom is $2.00\stackrel{\circ }{A}$ and its crystal structure is fcc lattice, what is the volume (in $c{m}^3$) of one unit cell?

1. $8.00\times {10}^{-24}$
2. $0.5\times {10}^{-23}$
3. $1.81\times {10}^{-22}$
4. $4.45\times {10}^{-23}$

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. Percentage of free space in a body centered cubic unit cell is

1. $30\%$
2. $28\%$
3. $30\%$
4. $32\%$

Q. A body centred cubic lattice is made up of hollow spheres of B. Spheres of solid A are present inside the hollow spheres of B. If the radius of A is half the radius of B, what is the ratio of the total volume of spheres of B unoccupied by A in a unit cell and the volume of the unit cell?

1. $\frac{7\pi \sqrt{3}}{64}$
2. $\frac{7\sqrt{3}}{128}$
3. $\frac{7\pi }{24}$
4. None of these

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.

Why can't cubic unit cells have end centered variation ?

Q. Expand each of the following condensed formulas into their complete structural formulas.
(a)$C{H}_{3}C{H}_{2}COC{H}_{2}C{H}_3$
(b)$C{H}_{3}CHCH(C{H}_2{)}_{3}C{H}_3$

Q.

Calculate the efficiency of packing in case of a metal crystal for

(i) Simple cubic

(ii) Body - centred cubic

(iii) Face-centred cubic (with the assumptions that atoms are touching each other).

Q. The $C{l}^{-}$ ions in the of NaCl lattice structure are present at:

1. Corners of the cube
2. Centres of faces of the cube
3. Corners as well as face centres of the cube
4. Edge centres of the cube

Q. What are the possible distances between 2 octahedral voids in FCC lattice?

Q. Vacant space in $bcc,fcc$ and simple cubic lattice respectively are:
[0.77 Mark]

1. $46.6\text{\%},26\text{\%}$ and $32\text{\%}$
2. $26\text{\%},32\text{\%}$ and $52.4\text{\%}$
3. $68\text{\%},74\text{\%}$ and $52.4\text{\%}$
4. $32\text{\%},26\text{\%}$ and $47.6\text{\%}$

Q.

If for any $\mathrm{fcc}$ lattice, the tetrahedral void number is always $$8$$ ? As the $\mathrm{fcc}$s ${\mathrm{Z}}_{\mathrm{eff}}$ is $$4$$ and remains constant, Justify

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.

What is voids

Q. An element crystallizes in BCC unit cell having molecular mass $50g/mol$ . Calculate the density of unit cell, if its edge length is $300pm$.
Take
$N_A=6\times {10}^{23}$

1. $1.71gc{m}^{-3}$
2. $3.42gc{m}^{-3}$
3. $12.34gc{m}^{-3}$
4. $6.17gc{m}^{-3}$

Q.

The volume of nucleus is ______ as compared to the volume of complete atom.

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. Titanium metal has a density of $4.54gc{m}^3$ and a unit cell volume of $7\times {10}^{-23}c{m}^3$. In which cubic unit cell does titanium crystallise?
Given : $\text{Molecular mass of}Ti=48gmo{l}^{-1}$

1. Hexagonal close packing
2. Face centred cubic
3. Simple Cubic
4. Body centred cubic

Q.

The general formula for calculating the volume of a unit cell is

1. volume of a unit cell = (mass)³

2. volume of a unit cell = (radius)³

3. volume of a unit cell = (edge length)³

4. volume of a unit cell = (density)³

Q.

Packing fraction is maximum in which of the following?

1. Face Centre Cubic

2. Body Centre Cubic

3. Simple Cubic Close packing

4. Hexagonal Close Packing

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

Q.

The number of Octahedral voids in a hexagonal primitive unit cell are:

Q. The decreasing order of the size of voids in a closed packed structure is 1) octahedral, tetrahedral, cubical, triangular 2)triangular, tetrahedral, octahedral, cubicle 3)octahedral, cubical, tetrahedral, triangular 4)cubical, octahedral, tetrahedral, triangular

Q. What percentage of crystal space in fcc arrangement is vacant?

1. 74%
2. 68%
3. 26%
4. 32%

Q.

The close packing represents ABC ABC...... order of

1. Face centred cubic packing

2. Simple cubic packing

3. Body centred cubic packing

4. Hexagonal cubic closed packing

Q. Explain the calculation of radius of tetrahedral void