Solid State Test

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Solid State Test - 23

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Weekly Quiz Competition

Question 1
1 / -0

An ionic compound XY forms a crystal structure in which 'Y' atoms form ccp lattice and 'X' atoms are sopositioned that each 'X'-atom touches 6'Y'-atoms. If the nearest distance between two 'X'-atoms is $$2\sqrt{2}$$ ,then the density ($$g/cm^{3}$$) of XY crystal is :

A
$$5\sqrt{6}$$

B
$$\frac{20}{3}$$

C
$$\frac{5}{6}$$

D
$$\frac{5}{3}$$

Solution

The nearest distance between two X-atom is $$\frac{a}{\sqrt{2}}$$
so $$\frac{a}{\sqrt{2}}$$ = $$2\sqrt{2}$$ and a = 4
d = $$\dfrac {z(molar mass)}{NA\times} a^3$$ = $$\dfrac {4\times {64}}{6\times 10^{23}}\times (4\times 10^{-8} )^{3}$$
= $$\frac{40}{6}$$
= $$\frac{20}{3}$$g/cm3
Question 2
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Analysis show that nickel oxide consist of nickel ion with 96% ions having $$d^a$$ configuration and 4% having $$d^7$$ configuration. Which amongst the following best represents the formula of the oxide?

A
$$Ni_{1.02}O_{1.00}$$

B
$$Ni_{0.96}O_{1.00}$$

C
$$Ni_{0.96}O_{0.98}$$

D
$$Ni_{0.98}O_{1.00}$$

Solution

Analysis show that nickel oxide consist of nickel ions with $$96\%$$ having
$$d^a$$ and $$4\%$$ $$d^7$$ configuration.
For $$Ni$$,
$$d^8\rightarrow Ni^{2+}, d^7\rightarrow No^{3+}$$.
Total charge of nickel.
$$(0.96\times 2)+(0.04\times 3)=2.04$$.
No. of $$O^{2-}ion=\frac {2.04}{2}=1.02$$.
Formula of solid $$=NiO_{1.02}=Ni_{0.98}O$$.
Question 3
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Consider a cube containing n unit cells of a cubic system. A plane ABCD obtained by joining the mid points of the edges on one of its identical faces had atoms arranged as shown. Let p be the packing fraction. Choose the correct option:

A
$$n=1, p=\frac {22}{21\sqrt 2}$$

B
$$n=8, p=\frac {11}{21}$$

C
$$n=8, p=\frac {11}{4}$$

D
$$n=1, p=\frac {11\sqrt 3}{28}$$

Solution

Cube which contains $$8$$ unit cell.
By observing face $$ABCP$$, we can say that the face of the cube look like in given figure by this $$PQRS$$ can be considered as a face of a unit cell which is a simple cubic arrangement. So $$n=8$$ for this cube.
Since only one atom is present in simple cubic. In simple cubic $$2r=a$$.
$$\therefore$$ Packaging fraction $$=\cfrac{\cfrac{4}{3}\pi r^3}{a^3}=\cfrac{\cfrac{4}{3}\pi \cfrac{a^3}{8}}{a^3}=\cfrac{4}{3}\times\cfrac{22}{7}\times \cfrac{1}{8}=\cfrac{11}{21}$$
Question 4
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Which one of the following is a pseudo solid?

A
Calcium fluoride

B
Glass

C
Sodium chloride

D
All of the above

Solution

Pseudo solid is a solid which possesses the property of liquids. Glass is a pseudo solid and in a very slow process, it flows like a liquid due to which the base of glass gets thicker than top.
Question 5
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The volume occupied by atoms in a simple cubic unit cell is (edge length $$=$$ a) :

A
$$a^{3}$$

B
$$\dfrac {4\pi a^{3}}{3}$$

C
$$\dfrac {\pi a^{3}}{6}$$

D
$$\dfrac {\sqrt {3}\pi}{8}$$

Solution

In simple cubic lattice, we have $$a = 2r$$
Volume $$ = \dfrac {4}{3} \pi r^3 = \dfrac {4}{3} \pi \left (\dfrac {a}{3}\right )^3 = \dfrac {1}{6} \pi a^3$$
Question 6
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Which of the following has a regular repeated molecular pattern in three dimensional space?

A
Solids and liquids

B
Liquids and gases

C
Solids

D
Gases

Solution

solids have a regular repeated molecular pattern in three dimensional space and this is due to their property of high intermolecular forces. But in liquids and gases the arrangement of molecular pattern it is irregular.

Hence, the correct option is $$(C)$$

Question 7

1 / -0

Statement 1: Distance between nearest lattice points in BCC is greater than the same in FCC having same edge length.
Statement 2: FCC has greater packing efficiency than BCC.

Statement-1 is true, statement-2 is true and statement-2 is the correct explanation for statement-1

Statement-1 is true, statement-2 is true and statement-2 is not the correct explanation for statement-1

Statement-1 is true, statement-2 is false

Statement-1 is false, statement-2 is true

Solution

Lattice type	Number of lattice points/atoms per units cell	Nearest distance between lattice points	Maximum packing density	Example
Simple cubic	$$\dfrac{1}{1}$$	$$a$$	$$\dfrac{\pi}{6} = 52\%$$	Phosphor
Body centered cubic	$$\dfrac{2}{2}$$	$$\dfrac{a\sqrt{3}}{2}$$	$$\dfrac{\pi\sqrt{3}}{8} = 86\%$$	Tungsten
Face centered cubic	$$\dfrac{4}{4}$$	$$\dfrac{a\sqrt{2}}{2}$$	$$\dfrac{\pi\sqrt{2}}{3} = 74\%$$	Aluminum
Diamond	$$\dfrac{4}{8}$$	$$\dfrac{a\sqrt{2}}{2}$$ Nearest distance between atoms: $$\dfrac{a\sqrt{3}}{4}$$	$$\dfrac{\pi\sqrt{3}}{16} = 34\%$$	Silicon

From the above table it can be seen that distance between BCC lattice points is greater than distance between FCC lattice points.
Also the packing efficiency of FCC is more than BCC but it is not the explanation of the previous statement.

Question 8
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The interstitial hole is called tetrahedral because :

A
it is formed by four spheres

B
partly same and party different

C
it is formed by four spheres, the centres of which from a regular tetrahedron

D
none of the above

Solution

The tetrahedral hole can be visualized as three spheres in a plane and one on top of it with the space at the centre having the shape of a regular tetrahedron.
Question 9
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Directions For Questions

Only those atoms which form four covalent bonds produce a repetitive three dimensional structure using only covalent bonds, e.g. diamond structure. The latter is based on a FCC lattice where lattice points are occupied by carbon atoms. Every atom in this structure is surrounded tetrahedrally by four others. Germanium, silicon and grey tin also crystallize in the same way as diamond. (Given: $$N_A=6\times 10^{23}, sin 54^o 44'=0.8164)$$.

...view full instructions

If edge length of the cube is $$3.60A^o$$, then radius of carbon atom is:

A
$$0.78A^o$$

B
$$0.92 A^o$$

C
$$0.64 A^o$$

D
$$0.35 A^o$$

Solution

Let the diameter of Carbon atom be $$d$$
$${4d}_c\quad sin\left(\cfrac {109}{2}\right)=\sqrt {2}a$$
$${4d}_c\quad sin(54^{\circ}44')=\sqrt {2}a$$
$$4\times d_c\times 0.8164=\sqrt {2}\times 3.6$$
$$d_c=1.56\mathring A$$
$$r_c=\cfrac {d_c}{2}=0.78\mathring A$$
Question 10
1 / -0

A unit cell of sodium chloride has four formula units. The edge of length of the unit cell is $$0.564$$ nm. What is the density (in g/cc) of sodium chloride?

A
$$1$$

B
$$2.16$$

C
$$4.32$$

D
None of the above

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Solid State Test - 23

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Solid State Test - 23

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Question 1

$$5\sqrt{6}$$

$$\frac{20}{3}$$

$$\frac{5}{6}$$

$$\frac{5}{3}$$

Solution

Question 2

$$Ni_{1.02}O_{1.00}$$

$$Ni_{0.96}O_{1.00}$$

$$Ni_{0.96}O_{0.98}$$

$$Ni_{0.98}O_{1.00}$$

Solution

Question 3

$$n=1, p=\frac {22}{21\sqrt 2}$$

$$n=8, p=\frac {11}{21}$$

$$n=8, p=\frac {11}{4}$$

$$n=1, p=\frac {11\sqrt 3}{28}$$

Solution

Question 4

Calcium fluoride

Glass

Sodium chloride

All of the above

Solution

Question 5

$$a^{3}$$

$$\dfrac {4\pi a^{3}}{3}$$

$$\dfrac {\pi a^{3}}{6}$$

$$\dfrac {\sqrt {3}\pi}{8}$$

Solution

Question 6

Solids and liquids

Liquids and gases

Solids

Gases

Solution

Question 7

Statement-1 is true, statement-2 is true and statement-2 is the correct explanation for statement-1

Statement-1 is true, statement-2 is true and statement-2 is not the correct explanation for statement-1

Statement-1 is true, statement-2 is false

Statement-1 is false, statement-2 is true

Solution

Question 8

it is formed by four spheres

partly same and party different

it is formed by four spheres, the centres of which from a regular tetrahedron

none of the above

Solution

Question 9

$$0.78A^o$$

$$0.92 A^o$$

$$0.64 A^o$$

$$0.35 A^o$$

Solution

Question 10

$$1$$

$$2.16$$

$$4.32$$

None of the above

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