The Solid State

Question 129
CBSEENCH12005477

Ferric oxide crystallizes in a hexagonal close packed array of oxide ions with two out of every three tetrahedral holes occupied by ferric ions. Derive the formula of the ferric oxide.

Solution

Let us Suppose the number of oxide (O2–) ions = N.
Number of octahedral void = number of anions
So that the number of octahedral voids = N
We have Given that
Two out of every three octahedral holes are occupied by ferric ions.
So that the number of ferric (Fe3+) ions = 2N/3
The ratio of the number of Fe3+ ions to the number of O2− ions,
Fe3+ : O2− = 2N/3 : N
Multiply 3 and divide by N we get
Fe3+ : O2− = 2 : 3
Hence, the formula of the ferric oxide is Fe2O3.

Question 130
CBSEENCH12005478

Classify each of the following as being either a p-type or an n-type semi conducor:
(i) Ge doped with In
(ii) B doped with Si.

Solution

(i) Ge is an element of 14th group (like Si) and has configuration 4s24p2. It has been doped with In, a 13th group element having 5s25p1 configuration i.e., element of 14th group has been doped with 13th group element. All three valence electrons of impurity atom (In) gets bonded with three out of four eectrons of Ge and one electron of Ge remains unbonded. Conductivity is due to unbonded electron of insulator, Ge. Therefore, it is a p-type semi-conductor.

(ii) Boron, B is an element of 13th group and has 2s22p1 configuration. It is doped with Si, an element of 14th group having 3s23p2 configuration. All three electrons of boron gets bonded with 3 out of 4 electrons of Si and 4th electron of impurity atom (i.e., Si) is responsible for conductivity. Thus it is a n-type semiconductor.

Question 131
CBSEENCH12005479

In terms of band theory, what is the difference between a conductor and an insulator?

Solution

Solution:

Molecular orbirals of metals are formed by atomic orbitals. These orbitals are so close to each other as they form band or valence band.

(i) Difference between conductor and insulator - In conductors there is no energy gap between the valence band, which facilitates the flow of electrons easily under an applied electric field and metals show conductivity.

While in insulators there is large energy gap between the valence band and electrons cannot jump to it i.e. large energy gap prevents the flow of electricity.

(ii)Difference between conductors and semiconductor - In conductors there is no energy gap between the valence band and conduction band, which facilitates the flow of electrons easily under an applied electric field and metals show conductivity.

While in semi conductors, there is small energy gap between valence bond and conduction band. The small gap between band facilitates some electrons to jump to the conduction band by acquiring extra energy.

Question 132
CBSEENCH12005480

In terms of band theory, what is the difference between a conductor and a semi-conductor?

Solution

Semiconductor: In instrinsic semiconductors, the energy gap, Eg, is relatively small (≈ = 1 eV). At absolute zero, conduction band is empty and valence band is full. Therefore, the solid behaves as an insulator at very low temperatures. However, at room temperature, some electrons from the top of valence band acquires enough thermal energy to jump into the conduction band. They leave behind a number of holes. Both electrons and holes movement contribute to conduction.
In extrinsic semi-conductor of n-type, the donor energy level is close to the bottom of conduction band.
In p-type the acceptor energy level is close to the top of valence band.

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