Chemistry

Solid State and Crystal Structures

151 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 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 chemistry p- block elements-ii compounds of phosphorus- pcl5 phosphorus halides compounds of phosphorus compounds of phosphorus - pcl3

The solid $PCl _5$ exists as :

  1. $PCl _3$
  2. $PCl _4^+$
  3. $PCl _6^-$
  4. $PCl _4^+$ and $PCl _6^-$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

In solid state, $PCl _5$  prefers to exist as oppositely charged ions like $[PCl _4]^+$ & $[PCl _6]^-$ as the ionic bonding enhances the crystalline nature.

Also, $[PCl _4]^+$ is tetrahedral while $[PCl _6]^-$ is octahedral, these structures fit well into each other providing extra stability to the soild structure.

Multiple choice chemistry p- block elements-ii compounds of phosphorus- pcl5 phosphorus halides compounds of phosphorus compounds of phosphorus - pcl3

Solid crystalline $PCI _5$ has structure which of the following?

  1. Bi-pyramidal

  2. Octahedral and tetrahedral ions

  3. Square-pyramidal

  4. Pentagonal

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

In solid state, $PCl _5$ prefers to exist as oppositely charged ions like $[PCl _4]^+$ & $[PCl _6]^-$ as the ionic bonding enhances the crystalline nature. Also, $[PCl _4]^+$ is tetrahedral while $[PCl _6]^-$ is octahedral, these structures fit well into each other providing extra stability to the soild structure.

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 nanochemistry nanotechnology applied chemistry materials chemistry

The size of nano materials lies between the width of ______ hydrogen atoms laid side by side.

  1. 1-5

  2. 4-25

  3. 100-150

  4. 1000-5000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The size of nanomaterials lies between the width of 4-25 hydrogen atoms laid side by side. 1 nm is the width of 4 hydrogen atoms placed side by side. Nanomaterials have atleast one dimension between 1 nm and 100 nm.

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 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 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.

Multiple choice imperfections in solids solid state the solid state chemistry

Calculate the dencity of NaCl type ionic solid AB($M _{w}$=60) in $gm/CM^{3}$ if shortest distance between two nearest neighbours is 100 pm &solid having $20\%$ schottky defect$(N _{A}=6\times10^{23}$)

  1. 10

  2. 20

  3. 30

  4. 40
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice imperfections in solids solid state the solid state chemistry

Give the correct order of initials T(true) or F(False) for following statements:
I. In an anti-fluorite structure, anions form FCC and cations occupy all the tetrahedral voids
II. If the radius of cation and anion is $20$ and $95$ pm, then the coordination number of the cation is the crystal is $4$.
III. An atom or ion is transferred from a lattice site to an interstitial position in Frenkel defect.
IV. The density of crystal always increases due to substitutional impurity defect.

  1. TTTT

  2. FFFF

  3. FFTT

  4. TFTF
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

I is False: In anti-fluorite, anions form FCC and cations occupy all tetrahedral voids. II is True: Radius ratio 20/95 = 0.21, which falls in the range for coordination number 4. III is True: This is the definition of Frenkel defect. IV is False: Density can decrease if the impurity atom is smaller or lighter.

Multiple choice imperfections in solids solid state the solid state chemistry

There are N atoms in a crystal with $N _1$ interstitial positions in its structure. If there are n Frenkel defects in the crystal, then n is equal to :

  1. $\left (\dfrac{N}{N _1} \right )^{\dfrac{1}{2}} exp^{(-E _i/2KT)}$
  2. $\left (\dfrac{N _1}{N}\right )^{\dfrac{1}{2}} exp^{(-E _i/2KT)}$
  3. $\left (\dfrac{N}{N _1}\right )^{\dfrac{1}{2}} exp^{(E _i/2KT)}$
  4. $\left (\dfrac {N _1}{N}\right )^{\dfrac{1}{2}} exp^{(E _i/2KT)}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

There are N atoms in a crystal with $N _1$ interstitial positions in its structure. If there are n Frenkel defects in the crystal, then n is equal to $\left (\dfrac{N}{N _1} \right )^{\dfrac{1}{2}} exp^{(-E _i/2KT)}$