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Element $'B'$ forms ccp structure and $'A'$ occupies half of the octahedral voids, while oxygen atoms occupy all the tetrahedral voids. The structure of bimetallic oxide is :

Option: 1 $A_{4}B_{2}O$
Option: 2 $AB_{2}O_{4}$
Option: 3 $A_{2}BO_{4}$
Option: 4 $A_{2}B_{2}O$

Voids -

Voids are empty spaces in a unit cell. They are of four types: triangular, tetrahedral, octahedral, cubic.

B forms ccp structure (FCC)

Number of atoms per unit cell of $'B'=\frac{1}{8}\times8+6\times\frac{1}{2}=4$

$'A'$ occupies half of the octahedral voids.

Number of atoms of element $A:-\; \; \frac{1}{2}\left [ 12\times\frac{1}{4}+1 \right ]$

$=\frac{1}{2}\times4=2$

$'O'$ atoms occupy all the tetrahedral voids.

Number of atoms of $\\O:-\; \; 8$

[2 Td voids on 4 Body diagonal]

Structure of bimetallic oxide is :-

$A_{2}B_{4}O_{8}=AB_{4}O_{4}$

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#Long answer type

A sample of ferrous oxide has actual formula $Fe_{0.93 }O_{1.00}$ . In this sample, what fraction of metal ions are $Fe^{2+}$ ions? What is the type of non-stoichiometric defect present in this sample?

Let the number of $O^{2-}$ be 100

Then number of $Fe^{2+}=x$

Number of $Fe^{3+}=93-x$

To maintain electrical neutrality net positive charge is equal to net negative charge

$2x+393-x=2\times 100$

$2x+279-3x=200$

$x=79$

$Fe^{2+}=79$

$\frac{Fe^{2+}}{Fe^{2+}+Fe^{3+}}=799$

$=0.849$

Metal deficiency defect is present in the sample because iron is less in amount than that required for stoichiometric composition.

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#Long answer type

How does the doping increase the conductivity of semiconductors?

Conductivity of semiconductors are exceptionally low for practical use. Semiconductors are doped to generate either a surplus or deficiency in valence electrons depending on whether n-type semiconductors are required or p-type. An electron rich or electron deficient impurity as compared to the intrinsic semiconductor, silicon or germanium is used for doping. Electronic defects are introduced in them by such impurities.

On doping silicon with electron rich impurities, the extra electron becomes delocalized increasing the conductivity of doped silicon. Hence silicon doped with electron-rich impurity is called n-type semiconductor due to the negatively charged electron. For ex. When group 15 elements are added to silicon
When silicon is doped with electron-deficit impurities to increase the conductivity through positive holes, this type of semiconductors are called p-type semiconductors. Ex. Addition of group 13 elements to group 14 element.

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#Long answer type

Show that in a cubic close packed structure, eight tetrahedral voids are present per unit cell.

In ccp, each unit cell consists of eight cubic components and the number of atoms per unit cell is given by

N_c*contribution+N_f*contribution

$=8\times \frac{1}{}8+6\times \frac{1}{2}=4$

The tetrahedral voids are positioned at the centre of cubic cell.

In cubic close packing number of tetrahedral voids per unit cell $= 8\times 1=8$

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#Long answer type

With the help of a labelled diagram show that there are four octahedral voids per unit cell in a cubic close packed structure.

In ccp, one octahedral void is present at the centre of body surrounded by six atoms at the centre of respective face.
Where N_c=Number of atoms at corner

N_f=Number of atoms at face centre

=N_c*contribution+N_f*contribution

$=8\times 18+6\times 12=4$

Position of octahedral voids=Edge centre and body centre

Number of octahedral voids per unit cell in cubic close packing= $Ne\times \frac{1}{4}+Nb\times 1=12\times \frac{1}{4}+1\times 1=4$

Number of octahedral voids=4

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#Assertion Reason type

In the following questions, a statement of Assertion (A) followed by a statement of Reason (R) is given. Choose the correct answer out of the following choices.
(a) Assertion and Reason both are correct statements and Reason is the correct explanation for Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation for Assertion.
(c) Assertion is correct but Reason is wrong.
(d) Assertion is wrong but Reason is correct.

Assertion (A): Semiconductors are solids with conductivities in the intermediate range from $10^{-6}-10^{4}ohm^{-1}m^{-1}$

Reason (R): Intermediate conductivity in semiconductor is due to partially filled valence band.

The answer is the option (c) Assertion is correct but Reason is wrong.
Conductance of semiconductors lies between metals and insulators, i.e., in the range of $10^{-6}-10^{4}ohm^{-1}m^{-1}$

Valence band is either filled or empty in semiconductors, it is the gas which is in between conductors and insulators.

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#Assertion Reason type

In the following questions, a statement of Assertion (A) followed by a statement of Reason (R) is given. Choose the correct answer out of the following choices.
(a) Assertion and Reason both are correct statements and Reason is the correct explanation for Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation for Assertion.
(c) Assertion is correct but Reason is wrong.
(d) Assertion is wrong but Reason is correct.

Assertion (A): The packing efficiency is maximum for the fcc structure.

Reason (R): The coordination number is 12 in fcc structures.

The answer is the option (b) Assertion and Reason both are correct statements but Reason is not the correct explanation for Assertion.

In fcc unit cell, there is ccp arrangement with packing efficiency of 74.01% which is maximum. In ccp arrangement, coordination number is 12.

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#Assertion Reason type

In the following questions, a statement of Assertion (A) followed by a statement of Reason (R) is given. Choose the correct answer out of the following choices.
(a) Assertion and Reason both are correct statements and Reason is the correct explanation for Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation for Assertion.
(c) Assertion is correct but Reason is wrong.
(d) Assertion is wrong but Reason is correct.

Assertion (A): Total number of octahedral voids present in unit cell of cubic close packing including the one that is present at the body centre, is four.

Reason (R): Besides the body centre, there is one octahedral void present at the centre of each of the six faces of the unit cell and each of which is shared between two adjacent unit cells.

The answer is the option (c)(c) Assertion is correct but Reason is wrong.

There are 12 octahedral voids at the edge centre and 1 in the body centre.
So total number of octahedral voids present in unit cell of cubic close packing = $12 \times \frac{1}{2} +1 = 4$

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infoexpert24

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#Assertion Reason type

In the following questions, a statement of Assertion (A) followed by a statement of Reason (R) is given. Choose the correct answer out of the following choices.
(a) Assertion and Reason both are correct statements and Reason is the correct explanation for Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation for Assertion.
(c) Assertion is correct but Reason is wrong.
(d) Assertion is wrong but Reason is correct.

Assertion (A): Graphite is a good conductor of electricity, however, diamond belongs to the category of insulators.
Reason (R): Graphite is soft in nature on the other hand diamond is very hard and brittle.

The answer is the option (b)Assertion and reason both are correct statements but reason is not correct explanation for assertion.

Diamond is a non-conductor of electricity because all valence electrons of carbon are involved in bonding and thus there is no delocalised electron in its structure. In graphite, one valence electron is free to move between adjacent layers making it a good conductor.
In Graphite, parallel layers are held together by week van der Waals force. That is why it is soft. However, diamond is hard since C atom is covalently bonded with the adjacent 3 carbon atoms forming a 3-dimensional network.

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infoexpert24

#Assertion Reason type

In the following questions, a statement of Assertion (A) followed by a statement of Reason (R) is given. Choose the correct answer out of the following choices.
(a) Assertion and Reason both are correct statements and Reason is the correct explanation for Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation for Assertion.
(c) Assertion is correct but Reason is wrong.
(d) Assertion is wrong but Reason is correct.

Assertion (A): The total number of atoms present in a simple cubic unit cell is one.
Reason (R): Simple cubic unit cell has atoms at its comers, each of which is shared between eight adjacent unit cells.

The answer is the option (a) (a) Assertion and Reason both are correct statements and Reason is the correct explanation for Assertion.
In simple cubic unit cell since only corners are occupied by atoms, the total number of atoms is $Z =\frac{1}{8} \times 8 =1$ and Simple cubic unit cell has atoms at its comers, each of which is shared between eight adjacent unit cells.

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Get Answers to all your Questions

All Questions

Element forms ccp structure and occupies half of the octahedral voids, while oxygen atoms occupy all the tetrahedral voids. The structure of bimetallic oxide is : Option: 1 Option: 2 Option: 3 Option: 4

Posted by

Ritika Jonwal

A sample of ferrous oxide has actual formula . In this sample, what fraction of metal ions are ions? What is the type of non-stoichiometric defect present in this sample?

Posted by

infoexpert24

Crack CUET with india's "Best Teachers"

How does the doping increase the conductivity of semiconductors?

Posted by

infoexpert24

Show that in a cubic close packed structure, eight tetrahedral voids are present per unit cell.

Posted by

infoexpert24

JEE Main high-scoring chapters and topics

With the help of a labelled diagram show that there are four octahedral voids per unit cell in a cubic close packed structure.

Element $'B'$ forms ccp structure and $'A'$ occupies half of the octahedral voids, while oxygen atoms occupy all the tetrahedral voids. The structure of bimetallic oxide is :

Option: 1 $A_{4}B_{2}O$
Option: 2 $AB_{2}O_{4}$
Option: 3 $A_{2}BO_{4}$
Option: 4 $A_{2}B_{2}O$

A sample of ferrous oxide has actual formula $Fe_{0.93 }O_{1.00}$ . In this sample, what fraction of metal ions are $Fe^{2+}$ ions? What is the type of non-stoichiometric defect present in this sample?