Chemistry

Solid State and Crystal Structures

198 Questions

Solid state chemistry focuses on the structural properties of crystalline solids. Questions cover Bravais lattices, unit cells, and close packed structures. This topic is essential for chemistry papers in UPSC and state PSC examinations.

Bravais lattice typesUnit cell calculationsClose packed structuresCrystal densityBragg's LawWurtzite structure

Solid State and Crystal Structures Questions

Multiple choice chemistry atomic theory, periodic classification and properties of elements introduction to periodic table necessity of classification need for classification

A metal crystallizes with a face-centred cubic lattice. The edge length of the unit cell is 408 pm. The diameter of the metal atom is:

  1. 228 pm

  2. 288 pm

  3. 144 pm

  4. 326 pm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In a face-centered cubic (FCC) lattice, the relation between edge length (a) and atomic radius (r) is a = 2 * sqrt(2) * r. The diameter (d) is 2r. Thus, d = a / sqrt(2). Given a = 408 pm, d = 408 / 1.414 = 288.5 pm, which rounds to 288 pm.

Multiple choice forces on solids elastic and plastic substances forces and matter properties of matter physics

According to $C.E$ van der Waal, the interatomic potential varies with the average interatomic distance $(R)$ as 

  1. $R^{-1}$
  2. $R^{-2}$
  3. $R^{-4}$
  4. $R^{-6}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

According to the relation

$ V(r)=\dfrac{-3}{4}\dfrac{{{\alpha }^{2}} _{0}l}{{{(4\pi {{\varepsilon } _{0}})}^{2}}{{R}^{6}}} $

$ V(r)\propto \dfrac{1}{{{R}^{6}}} $

$ V(r)\propto {{R}^{-6}} $


Multiple choice physics magnetism and matter magnetic materials behaviour of substances in magnetic field classification of magnetic materials

A domain in ferromagnetic iron is in the form of a cube of side length $2$ $\mu m$ then the number of iron atoms in the domain are (Molecular mass of iron $=55$g $mol^{-1}$ and density $=7.92$g $cm^{-3}$)

  1. $6.92\times 10^{12}$ atoms
  2. $6.92\times 10^{11}$ atoms
  3. $6.92\times 10^{10}$ atoms
  4. $6.92\times 10^{13}$ atoms
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The volume of the cubic domain
$V=(2\mu m)^3=(2\times 10^{-6}m)^3$
$=8\times 10^{-18}m^3=8\times 10^{-12}cm^3$
and mass $=$volume $\times$ density
$=8\times 10^{-12}cm^3\times 7.9g cm^{-3}$
$=63.2\times 10^{-12}$g
Now the Avagadro number $(6.023\times 10^{23})$ of iron atoms have a mass of $55$g. Hence the number of atoms in the domain are.
$N=\dfrac{63.2\times 10^{-12}\times 6.023\times 10^{23}}{55}=6.92\times 10^{11}$ atoms.

Multiple choice chemistry lattice energy defining lattice energy ionic or electrovalent bond energy cycles

The relation between the magnitudes of lattice energy of crystal and its formation energy is:

  1. lattice energy > formation energy
  2. lattice energy $=$ formation energy

  3. lattice energy < formation energy

  4. none of the above
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Lattice energy is the energy required to break apart an ionic solid and convert its component atoms into gaseous ions. The value of the lattice energy to always be positive.

Also, enthalpy of lattice formation is defined as the energy released when gaseous ions bind to form an ionic solid. The value is negative but has the same magnitude as lattice energy.
Hence, $B$ is correct.

Multiple choice chemistry solid state electrical and magnetic properties of solids impurity defects properties of solids

The density for simple cubic lattice is :


[where A is atomic weight, N is the Avogadro number and a is lattice parameter]

  1. $\displaystyle \frac{4A}{Na^3}$
  2. $\displaystyle \frac{2A}{Na^3}$
  3. $\displaystyle \frac{A}{Na^3}$
  4. $\displaystyle \frac{A}{Na^2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Density = $\displaystyle \frac{\text{Mass of atom in unit cell}}{{\text{Total volume of unit cell}}} = \cfrac{nM}{V _cN _A} $


For simple cubic lattice, 

$n = 1  \\   V _c = a^3  \\$

$Given,  M = A$

$= \cfrac{A}{Na^3}$

Multiple choice chemistry solid state electrical and magnetic properties of solids impurity defects properties of solids

Frenkel defect is observed in:

  1. $MgCl _2$
  2. $AgCl$
  3. $ZnS$
  4. $AgI$
Reveal answer Fill a bubble to check yourself
B,C,D Correct answer
Explanation

Frenkel defect is the defect which is created when an ion leaves its appropriate site in the lattice and occupies an interstitial site. A hole or vacancy is thus produced in the lattice.


Frenkel defect is exhibited in ionic compounds in which the radius ratio is low. The cations and anions differ much in their sizes and the ions have low co-ordination numbers. Examples are ZnS, AgBr, AgI, AgCl.

Multiple choice physics physical quantities and measurement measurement of small and large distances measurement of distance unit of fundamental quantities

100 kg of Silver has volume $10{ m }^{ 3 }.$ The density of silver in C.G.S is

  1. $10{ g/cm }^{ 3 }$
  2. $0.05{ g/cm }^{ 3 }$
  3. $0.01{ g/cm }^{ 3 }$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation
Given

The mass of silver $= 100 kg$

Volume of the cube $= 10 m^3$

We know that the density of a substance is given by the following formula

$Density = \dfrac{Mass}{Volume}$

Density of the silver $= \dfrac{100}{10} kg/m^3=10kg/m^3$

Now we know that $1 kg = 1000 gm = 10^3 gm$

and $1 m = 100 cm$

$⇒ 1 m^3 = 100^3 \,cm^3 = 10^6 cm^3$

Therefore, the density of silver in cgs $= \dfrac{10\times 10^3}{10^6} gm/cm^3=0.01\,gm/cm^3$
Multiple choice chemistry the s-block elements (alkali and alkaline earth metals) anomalous properties of lithium group 1 elements: alkali metals properties of s block elements

Lithium selenide can be described as a cubic closest-packed array of selenide ions with lithium ions in all of the tetrahedral holes. Formula of lithium selenide is 

  1. $L{i _2}Se$
  2. $LiSe$
  3. $LiS{e _2}$
  4. $L{i _3}Se$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Answer(A):- $Li _2Se$

If number of Se =Z , Number of Li = 2Z

Multiple choice chemistry the s-block elements (alkali and alkaline earth metals) anomalous properties of lithium group 1 elements: alkali metals properties of s block elements

Lithium borohydride, $LiB{H} _{4}$, crystallizes in an orthorhombic system with four molecules per unit cell. The unit cell dimensions are $a=6.0\mathring { A } ,b=4.4\mathring { A } ,c=7.5\mathring { A } $. The density of crystals is
$\left( Li=7,B=11,{ N } _{ A }=6\times { 10 }^{ 23 } \right) $

  1. $0.74g/{cm}^{3}$
  2. $1.48g/{cm}^{3}$
  3. $0.37g/{cm}^{3}$
  4. $0.90g/{cm}^{3}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Using the density formula: d = (Z × M) / (NA × a × b × c). With Z=4, M=22 g/mol (7+11+4), NA=6×10^23, dimensions in Angstroms (1 Å = 10^-8 cm): volume = 6×4.4×7.5 × 10^-24 cm^3 = 198×10^-24 cm^3. Mass = (4 × 22)/(6 × 10^23) g = 1.47×10^-22 g. Density = 1.47×10^-22 / 198×10^-24 = 0.74 g/cm^3.

Multiple choice physics semiconductors band theory of solids, a brief introduction electron energies in solids energy bands

Which of the following has least band gap energy at $273K$.

  1. InSb

  2. InAs

  3. InP

  4. GaSb
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The energy gaps of the given semiconductors at $273K$ are given:

   $InSb=0.16eV$ (Indium antimonide),
   $InAs=0.33eV$ (Indium arsenide),
   $InP=1.29eV$ (Indium phosphide),
  $GaSb=0.67eV$ (Galiumium antimonide),
It is clear that $InSb$ has the least energy gap.

Multiple choice imperfections in solids solid state the solid state chemistry

The type of defect in $Nacl$ crystal will be -

  1. point defect

  2. interstitial will be

  3. vacancy defect

  4. impurity defect
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

NaCl is an ionic crystal that typically exhibits Schottky defects, which are a type of vacancy defect where ions are missing from their lattice sites.

Multiple choice imperfections in solids solid state the solid state chemistry

In a non-stochiometric sample of cuprons sulphide, with the composition $Cu _{1.8}$, cupric ions are also present in the lattice. The mole % of $Cu^{2+}$ present in the copper content of the crystal is:

  1. $99.9$%
  2. $11.11$%
  3. $88.88$%
  4. $18$%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$180 \ Cu$ atoms are associated with $100 \ S$ atoms.

Let $x$ atoms be present as $Cu^{+}$
Total charge on $xCu^+$ and $(180-x)Cu^{2+}$ must be equal to total charge on $100 \ S^{2-}$ ions.
So, $x+2(180-x)=2 \times 100$
$x+360-2x=200$
$x=160$
% of $Cu^{+}$ ions $= \cfrac {160}{180} \times 100=88.9$%

Multiple choice imperfections in solids solid state the solid state chemistry

The mineral hawleyite, one form of $CdS$, crystallizes in one of the cubic lattices , with edge length 5.87 A The density of hawleyite is $ 4.63 g cm^{-3} $
In which cubic lattice does hawleyite crystallizes?

  1. end centred cubic

  2. body centered cubic

  3. face centred cubic

  4. edge centred cubic
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Density of Howlegite $=4.63g/{ cm }^{ 3 }$  $(P)$

Edge length $={ 5.87A }^{ 0 }=5.87\times { 10 }^{ -8 }cm$ $(a)$
Density $\left( P \right) =\dfrac { z\times { a }^{ 3 }\times { N } _{ 0 } }{ M } $                                 $M=$ Molar mass of $cds=144g/mol$
$z=\dfrac { 4.63\times { \left( 5.87\times { 10 }^{ -8 } \right)  }^{ 3 }\times 6.02\times { 10 }^{ 23 } }{ 144 } $        $N=$ Avagadro Number $=6.023\times { 10 }^{ 23 }$
$=3.9\cong 4\quad \quad z=4$
$\therefore$   There are four formula units of cds present in on unit cell.
$\Rightarrow $  Face entered cubic lattice.