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 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
D Correct answer
Multiple choice imperfections in solids solid state the solid state chemistry

According to recent studies which of the following interstitial hydrides have simi-lattices that of their parent metals

  1. $La, Yb, W$
  2. $Yb, W, V$
  3. $V, I, a$
  4. $N, Pd, Ce, Ac$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

La, Yb, and W are known to form interstitial hydrides where the metal lattice remains essentially unchanged.

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

The compounds having the general molecular formula $A^{2+ }Fe _{2.047}$are called Ferrites.

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$General\; formula\; of\; Ferrites\; is\; { m }^{ 2+({ Fe } _{ 2 }{ O } _{ 4 }) }\ \; \; \; eg.\; \; ZnF{ e } _{ 2 }{ O } _{ 4 }\ Hence\; the\; above\; statement\; is\; false.$

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 $\left (\dfrac{N}{N _1} \right )^{\dfrac{1}{2}} exp^{(-E _i/2KT)}$

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 lattice and cations occupy all tetrahedral voids.
II. If the radius of cations and anions are $0.2\ \mathring A$ and $0.95\ \mathring A$, then co-ordination number of cation in the crystal is $4$.
III. An ion is transferred from a lattice site to an interstitial position in Frenkel defect.
IV. Density of crystal always increases due to substitutional impurity defect.

  1. TFFF

  2. FTTF

  3. TFFT

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

I. In an anti-flourite structure, anions form FCC lattice and cations occupy all tetrahedral voids.


II. Ratio of radius $= \dfrac{0.2}{0.95} = 0.21$ which lies between $0.155-0.225$ and so, it has co-ordination number of $3$.


III. Frenkel defect is a 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.

IV. The density of crystal may increase/decrease due to substitutional impurity defect.


Hence, the correct option is $\text{D}$

Multiple choice imperfections in solids solid state the solid state chemistry

Frenkel defect is found in crystals in which the radius ratio is:

  1. low
  2. $1.3$
  3. $1.5$

  4. slightly less than unity
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

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. However, in Schottky defect the size of cation and anion

are almost same, ex- KCl, AgBr.
Hence, the correct option is $\text{A}$

Multiple choice imperfections in solids solid state the solid state chemistry

In a solid lattice, the cation has left a lattice site and is located at an interstitial position. The lattice defect is known as____________.

  1. Interstitial defect

  2. Valency defect

  3. Frenkel defect

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

Frenkel defect is a 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.
The electroneutrality of the crystal is maintained since the number of positive and negative ions is the same. Since positive ions are small in size, they usually leave their positions in the lattice and occupy interstitial positions.

Multiple choice imperfections in solids solid state the solid state chemistry

What type of crystal defect is indicated in the diagram below?

$Na^{+}$ $Cl^{-}$ $Na^{+}$ $Cl^{-}$ $Na^{+}$ $Cl^{-}$
$Cl^{-}$ $Cl^{-}$ $Na^{+}$ $Na^{+}$
$Na^{+}$ $Cl^{-}$ $Cl^{-}$ $Na^{+}$ $Cl^{-}$
$Cl^{-}$ $Na^{+}$ $Cl^{-}$ $Na^{+}$ $Na^{+}$

  1. Frenkel defect

  2. Schottky defect

  3. Interstitial defect

  4. Frenkel and Schottky defects
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Schottky defect is indicated in the diagram as equal number of sodium cation and chloride anion are missing.
In Frenkel defect, a cation or anion leaves its regular site and occupies interstitial position.

Multiple choice imperfections in solids solid state the solid state chemistry

Which of the following exhibit Frenkel defect?

  1. $KBr$
  2. $AgBr$
  3. $AgCl$
  4. $ZnS$
Reveal answer Fill a bubble to check yourself
A,B,C,D Correct answer
Explanation

$KBr, AgBr, AgCl\ and\ ZnS$ exhibit Frenkel defect.
$AgBr$ also exhibits schottky defect.
$NaCl, KCl, CsCl$ etc, exhibits schottky defect.

Multiple choice imperfections in solids solid state the solid state chemistry

Which kind of defect is shown by the given crystal?
${ K }^{ + }$  ${ Cl }^{ - }$   ${ K }^{ + }$   ${ Cl }^{ - }$   ${ K }^{ + }$     ${ Cl }^{ - }$
${ Cl }^{ - }$  $\Box $      ${ Cl }^{ - }$    ${ K }^{ + }$   $\Box $       ${ K }^{ + }$
${ K }^{ + }$   ${ Cl }^{ - }$   $\Box $     ${ Cl }^{ - }$     ${ K }^{ + }$    ${ Cl }^{ - }$ 
${ Cl }^{ - }$   ${ K }^{ + }$   ${ Cl }^{ - }$   ${ K }^{ + }$   $\Box $        ${ K }^{ + }$   

  1. Schottky defect

  2. Frenkel defect

  3. Schottky Frenkel defects

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

In the given crystal equal number of cations and anions are missing (two ${K}^{+}$ and two ${Cl}^{-}$) from their normal lattice sites and the crystal maintains electrical neutrality. Hence, this is Schottky defect.

Multiple choice imperfections in solids solid state the solid state chemistry

Which of the following defect is seen in $FeO$? 

  1. Metal excess defect

  2. Metal deficiency defect

  3. Displacement defect

  4. Impurity defect
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$FeO$ has metal deficiency defect. Metal deficiency defect is supposed to arise when there are lesser number of positive ions than negative ions. In case of $FeO$, the positive ions are missing from their lattice sites. 

The additional negative charge is balanced by some nearby metal ion by acquiring one more positive charge. It happens in $FeO$ because $Fe$ has capacity of showing variable oxidation states.

Multiple choice imperfections in solids solid state the solid state chemistry

In a crystal, at $827^{\circ}C$, one out of $10^{10}$ lattice site is found to be vacant, while in the same solid, one out of $2 \times 10^9$ lattice site is found to be vacant at $927^{\circ}C$. What is the enthalpy of vacancy formation in kJ/mol unit?

  1. $76.8$
  2. $176.8$
  3. $33$
  4. $23$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$\cfrac {^nV}{N}=Ae^{-\Delta H _V/RT} \longrightarrow (x)$

$\left(\cfrac {^nV}{N}\right) _{827^oC}=\cfrac {1}{10^{10}} \longrightarrow (1)$
$\left(\cfrac {^nV}{N}\right) _{927^oC}= \cfrac {1}{2 \times 10^9} \longrightarrow (2)$                                   $\therefore T _1= 827+273=1100K ; T _2=927+273=1200K$

$\Rightarrow \cfrac {(2)}{(1)}= \cfrac {1/2\times 10^9}{1/10^{10}}= \cfrac {10^ {10}}{2 \times 10^9}= 0.5 \times 10=5$
$x \Rightarrow 2.303 \log 5= - \cfrac {\Delta H _V}{R} \left(\cfrac {1}{T _1}-\cfrac {1}{T _2}\right)$
$\therefore \Delta H _V= 2.303 \times \log 5 \times 8.314 \times \left(\cfrac {1100\times 1200}{100}\right)$
               $=1.766 \times 10^5 J$
               $=176.6kJ/mol$ $unit$ .

Multiple choice imperfections in solids solid state the solid state chemistry

Calcium crystallizes in a face centred cubic unit cell with a $=0.556$ nm. Calculate the density if it contains:

(i) $0.1\%$ Frenkel defect
(ii) $0.1\%$ Schottky defect

  1. $1.546, 1.546$
  2. $1.546, 1.544$
  3. $15.46, 15.46$
  4. $21.76, 41.66$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

$1.$ In frenkel defect there is no change in original density

$\rho=\cfrac{Z\times M _A}{N _A\times a^3}$
$\implies \rho=\cfrac{4\times 40}{6.023\times 10^{23}\times 171.8\times 10^{-24}}$
$\implies \rho=1.546$ $g/cm^3$

$2.$ In schottky defect $Z _{eff}$ changes so density changes
$Z _{new}=4-\cfrac{4\times 0.1}{100}=3.996$
$\rho =\cfrac { Z\times M _{ A } }{ N _{ A }\times a^{ 3 } } $
$\implies \rho =\cfrac { 3.996\times 40 }{ 6.023\times 10^{ 23 }\times 171.8\times 10^{ -24 } } $
$\implies \rho =1.544$$g/cm^{ 3 }$