Solid State Test

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Solid State Test - 26

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Question 1
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Directions For Questions

Packing fraction of a unit cell is defined as the fraction of the total volume of the unit cell occupied by the atom(s).$$\displaystyle \text{Packing fraction (P.F)} = \dfrac{\text{Volume of the atom (s) present in a unit cell}}{\text{Volume of unit cell}}$$ $$=\dfrac {Z \times \dfrac{4}{3} \pi r^{3}}{a^{3}}$$ Percentage of empty space $$=100-\text{P.F}\times 100$$ where $$Z$$ is the effective number of atoms in a cube, $$r$$ is the radius of an atom and $$a$$ is the edge length of the cube.

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Percentage of empty space in body centered cubic unit cell is nearly:

A
$$52.36$$

B
$$68$$

C
$$32$$

D
$$26$$

Solution

In body centered cubic unit cell, $$z =2 $$ and
$$ \sqrt{3} a = 4r $$
$$ P.F. = \dfrac {2 \times \dfrac{4}{3} \pi r^3}{a^3} $$
$$ P.F. = \dfrac {2 \times \dfrac{4}{3} \pi r^3}{64r^3} \times 3 \sqrt 3 $$
$$ P.F. = 68 \% $$
And hence empty space = $$32 \% $$
Question 2
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If $$a$$ is the edge length, first three nearest neighbour distances for primitive cubic lattice are, respectively:

A
$$a,$$ $${\sqrt 2a},$$ $${\sqrt 3a}$$

B
$${\sqrt3a},$$ $${\sqrt2a},$$ $$a$$

C
$$a,$$ $${\sqrt2a},$$ $$2a$$

D
$$a,$$ $${\sqrt 3a},$$ $$2a$$

Solution

First three nearest neighbor distances for primitive cubic lattice are, respectively, (edge length of unit cell $$=a$$) $$a,$$ $${\sqrt 2a},$$ and $${\sqrt 3a}$$.
Question 3
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The density of a pure substance A whose atoms are in cubic closed packed arrangement is $$1$$ g/cc. If all the tetrahedral voids are occupied by B atoms, what is the density (in g cm$$^{-3}$$) of resulting solid?[Atomic mass of $$A=30$$ g/mol and atomic mass of $$B=50$$ g/mol]

A
$$3.33$$

B
$$4.33$$

C
$$2.33$$

D
$$5.33$$

Solution

The formula for density is given below:

$$d=\dfrac{nM}{VN_A}$$ and therefore, $$ V = \dfrac{4\times 30}{1\times N_A}$$

After adding B,

$$d= \dfrac{(4\times 30+8\times 50)}{VN_A} = \dfrac{520}{120} = 4.33$$ (CCP has $$8$$ tetrahedral voids.)

Therefore, the density is $$4.33$$ g cm$$^{-3}$$.

Option B is correct.
Question 4
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Select the correct statement(s) :

A
The co-ordination number of each type of ion in a CsCl crystal is twelve.

B
A metal that crystallizes in a bcc structure has a co-ordination number of twelve.

C
A unit cell of an ionic crystal shares some of its ions with other unit cells.

D
The length of the unit cell in NaCl is $$552$$ pm (given that $${r_{Na+}= 85}$$ pm and $${r_{Cl-}= 181}$$ pm).

Solution

The co-ordination number of each type of ion in a CsCl crystal is $$8$$.

A metal that crystallizes in a bcc structure has a co-ordination number of $$8$$.

The length of the unit cell in NaCl is $$532$$ pm (given that $${r_{Na+}= 85}$$ pm and $${r_{Cl-}= 181}$$ pm).

Therefore, edge length $$=2r+2R = 2\times 85+2\times 181 = 532$$ pm

A unit cell of an ionic crystal shares some of its ions with other unit cells like face molecules are shared by $$2$$ unit cells and corner molecules are shared by $$8 $$ unit cells.

Option C is correct.
Question 5
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Graphite has hcp arrangement of carbon atoms and the parallel planes are $$3.35$$ $$\mathring A$$ apart. The density (in g cm$$^{-3}$$) of graphite is :

A
$$2.46$$

B
$$2.12$$

C
$$1.20$$

D
$$1.41$$

Solution

One unit cell of graphite contains $$4$$ C atoms. Thus, $$Z=4$$
The formula mass of graphite is $$12$$ g/mol.
Avogadro's number is $$N_o = 6.023 \times 10^{23}$$
The edge length is $$a=3.35\ A^{o}$$
The density of graphite $$=\dfrac {Z \times \text{formula mass}} {N_o \times a^3}=\dfrac {4 \times 12} {6.023 \times 10^{23} \times (3.35 \times 10^{-8})^3}=2.12$$ g/cc
Question 6
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The density for an FCC lattice is:

[A = atomic wt, N = Avogadro's number, a = lattice parameter]

A
$$\displaystyle \frac{4A}{Na^3}$$

B
$$\displaystyle \frac{2A}{Na^3}$$

C
$$\displaystyle \frac{A}{Na^3}$$

D
$$\displaystyle \frac{A}{Na^2}$$

Solution

In $$FCC$$ lattice, the no. of atoms per unit cell $$= 4$$

Density $$=\displaystyle \frac{mass\ of\ unit\ cell}{volume \ of\ unit\ cell} = \frac{4 A/N}{a^3} = \frac{4A}{Na^3}$$
Question 7
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Which of the following is not an amorphous substance?

A
Copper

B
Rubber

C
Glass

D
Polymers

Solution

The amorphous substance is defined as any noncrystalline solid in which the atoms and molecules are not organized in a definite lattice pattern. As Rubber, Glass and Polymers of high molecular mass are examples of amorphous solids and Copper is not an amorphous substance.
Copper is an example of a crystalline solid.
Hence, the correct option is $$A$$
Question 8
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If $$A$$ is the atomic mass number of an element, $$N$$ is the Avogadro number and $$a$$ is the lattice parameter, then the density of the element, if it has bcc crystal structure, is_________.

A
$$\displaystyle \dfrac{A}{Na^3}$$

B
$$\displaystyle \dfrac{2A}{Na^3}$$

C
$$\displaystyle \dfrac{\sqrt 3 A}{Na^3}$$

D
$$\displaystyle \dfrac{2\sqrt 2A}{Na^3}$$

Solution

$$\displaystyle d = \dfrac{Z \times A}{N \times a^3}$$

$$For\ bcc, Z = 2$$

$$\displaystyle d = \dfrac{2A}{Na^3}$$
Question 9
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Correct order for lattice energy of the given crystals is :

A
$$KCl < NaCl < NaF$$

B
$$NaF > KCl > NaCl$$

C
$$KCl > NaCl > NaF$$

D
$$NaF < NaCl < KCl$$

Solution

Lattice energy is directly proportional to the charge of the ion and inversely proportional to the size of ion.

As $$F^{-}$$ is smaller in size than $$Cl^-$$.

$$NaF$$ has greater lattice energy than $$NaCl$$ and as $$Na^{+}$$ is smaller in size than $$K^+$$.

Therefore, $$NaCl$$ has greater lattice energy than $$KCl$$.

So $$KCl<NaCl<NaF$$.

Hence, option B is correct.
Question 10
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Lattice energy of NaCl is $$-186$$ kcal/mol. If solution enthalpies of Na$$+$$ and Cl$$^-$$ are $$-97$$ kcal/mol and $$-85$$ kcal/mol respectively. The enthalpy NaCl solution in kcal will be:

A
$$-4$$

B
$$182$$

C
$$368$$

D
$$4$$

Solution

The enthalpy of solution of NaCl in kcal is:

$$\displaystyle \Delta H_{solution} = \Delta H_{\text {solution of cation}} + \Delta H_{\text {solution of anion}} - \Delta H_{\text {Lattice energy of NaCl}}$$

$$\Delta H_{solution}= (-97) + (-85) - (-186)=4$$ kcal/mol

The enthalpy change of solution refers to the amount of heat that is released or absorbed during the dissolving process (at constant pressure). This enthalpy of solution (ΔHsolution) can either be positive (endothermic) or negative (exothermic).

Hence, the correct option is $$D$$

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Solid State Test - 26

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Solid State Test - 26

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Question 1

$$52.36$$

$$68$$

$$32$$

$$26$$

Solution

Question 2

$$a,$$ $${\sqrt 2a},$$ $${\sqrt 3a}$$

$${\sqrt3a},$$ $${\sqrt2a},$$ $$a$$

$$a,$$ $${\sqrt2a},$$ $$2a$$

$$a,$$ $${\sqrt 3a},$$ $$2a$$

Solution

Question 3

$$3.33$$

$$4.33$$

$$2.33$$

$$5.33$$

Solution

Question 4

The co-ordination number of each type of ion in a CsCl crystal is twelve.

A metal that crystallizes in a bcc structure has a co-ordination number of twelve.

A unit cell of an ionic crystal shares some of its ions with other unit cells.

The length of the unit cell in NaCl is $$552$$ pm (given that $${r_{Na+}= 85}$$ pm and $${r_{Cl-}= 181}$$ pm).

Solution

Question 5

$$2.46$$

$$2.12$$

$$1.20$$

$$1.41$$

Solution

Question 6

$$\displaystyle \frac{4A}{Na^3}$$

$$\displaystyle \frac{2A}{Na^3}$$

$$\displaystyle \frac{A}{Na^3}$$

$$\displaystyle \frac{A}{Na^2}$$

Solution

Question 7

Copper

Rubber

Glass

Polymers

Solution

Question 8

$$\displaystyle \dfrac{A}{Na^3}$$

$$\displaystyle \dfrac{2A}{Na^3}$$

$$\displaystyle \dfrac{\sqrt 3 A}{Na^3}$$

$$\displaystyle \dfrac{2\sqrt 2A}{Na^3}$$

Solution

Question 9

$$KCl < NaCl < NaF$$

$$NaF > KCl > NaCl$$

$$KCl > NaCl > NaF$$

$$NaF < NaCl < KCl$$

Solution

Question 10

$$-4$$

$$182$$

$$368$$

$$4$$

Solution

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