Que 1: What is black body and black body radiation? Explain.
Ans: Black body: A perfect black body is one, which absorbs radiation of all wavelength’s incident upon it.
The term comes from the fact that a cold blackbody appears visually black. The black body is a composed of atoms and molecules which can emit and absorb light.
As the radiating power of a body is proportional to its absorbing power, a black body would also radiate more strongly at any given temperature than any other surface. They emit light because they are wiggling around due to their heat content (thermal energy). So a blackbody emits a certain spectrum of light that depends only on its temperature. The higher the temperature, the more light energy is emitted and the higher the frequency (shorter the wavelength) of the peak of the spectrum. The radiations emitted from the black body are independent of the nature of the body.
Que 2: Discuss the Energy distribution curve for a Black body radiation with necessary diagram.
Ans: As the radiating power of a body is proportional to its absorbing power, a black body would also radiate more strongly, at any given temperature than any other surface. The radiations are independent of the nature of the body and depend only on the temperature of the black body.
The distribution of energy in the radiation spectrum of black body is of the form of the curves
The different curves correspond to different temperatures of the black body. The following are the conclusions obtained from the above graph
1. The distribution of the energy is not uniform.
2. For a particular temperature, the intensity of radiation increases upto a particular wavelengthand then it is found to decrease with increase in wavelength.
3. As temperature increases, the peak energy shifts towards shorter wavelengths.
4. As the temperature increases, the area under each curve increases. It shows that, the rate ofemission increases very rapidly as the temperature rises.
Que 3: What is Compton Effect? Explain with diagram.
Ans: When a monochromatic beam of high frequency radiations (e.g. X-rays and prays) is scattered by a substance of less atomic number, the scattered radiations contain the radiations of higher wavelength along with the radiations of unchanged wavelength (or frequency). This phenomenon is called the Compton Effect.
The photon move with velocity of light ‘e’ possess momentum and obey all the laws of conservation of energy and momentum when they strike with electrons of the scattering substances.
When a photon of energy hu collides with the free electron of the scattering substance initially at rest, it transfers some of the energy to electron. Due to this energy, the electron gains kinetic energy and recoils with velocity v. Hence the scattered photon will have lower energy i.e. lower frequency or longer wavelength than incident one.
$$E = h ν=\frac{hc}{λ}$$
Basic assumption adopted for Compton scattering:
1. Compton effect is a result of interaction of a individual photon and free electron of target
2. The collision is relativistic and elastic
3. The laws of conservation of linear momentum and energy are valid.
Que 4: What is Photon? Mention the important Properties of Photon.
Ans: Photon, also known as light quantum, is a minute energy packet of electromagnetic radiation
Properties of Photon:
1. The existence of photon and electron are same in nature
2. The energy of one photon is E = h ν
3. The rest mass of the photon is zero and they travel with the speed of lights
4. The relation between energy and momentum of a photon
$$E = cp$$
$$\frac{hν}{c}=p$$
5. Photons are not affected by either an electric field or magnetic field (i.e. they are electrically neutral)
Que 5: Derive the time independent and time dependent Schrodinger wave equation for a particle having mass m and velocity v.
Ans: Schrodinger time independent equation
Let us consider a particle of mass m, moving with a velocity v. Let 𝚿 be the wave function of the particle along x, y and z coordinate axes at any time t. The de-Broglie wavelength associated with h/mv it is given by $$λ =\frac{h}{mv}$$
The classical differential equation of a progressive wave, moving with a wave velocity v can be written as
$$\frac{∂^{2}𝚿}{∂x^{2}}+\frac{∂^{2}𝚿}{∂y^{2}}+\frac{∂^{2}𝚿}{∂z^{2}}=\frac{1}{v^{2}}\frac{∂^{2}𝚿}{∂t^{2}}–(1)$$
The solution for equation (1) is assumed to be $$𝚿 = 𝚿_{0} e^{-iωt}—–(2)$$
where Wo is the amplitude of the wave at the point (x, y, z). It is a function of position. Differentiating equation (2) with respect to ‘t’ twice, we get
$$\frac{∂𝚿}{∂t}= 𝚿_{0} e^{-iωt}(-iω)$$
$$\frac{∂𝚿}{∂t}=-iω𝚿\,—–(3)$$and
$$\frac{∂^{2}𝚿}{∂x^{2}}=-ω^{2}𝚿\,—-(4)$$
Substituting equation (4) in (1), we get
Que 6: Differentiate between conductors, semiconductors and Insulators.
Ans:
| Conductor | Semiconductor | Insulator |
| Good Conductor of electricity | Behave as a Insulator at 0 K Temperature | Bad conductor of Electricity |
| CB and VB are partially filled | VB is completely filled CB is completely empty | VB is completely filled CB is completely empty |
| Energy gap = 0 eV | Energy gap ~ 1 eV | Energy gap ~ 6 – 7 eV |
| Conductivity decreases with increase in Temperature (Linearly) | Conductivity increases with increase in Temperature (Exponentially) | Conductivity increases with increase in Temperature (Exponentially) |
| Ex : Au, Ag, Cu | Ex: Ge, Si | Ex: Diamond, glass |
Que 7: What do you mean by Semiconductor?
Ans: A semiconductor is a type of material that has an intermediate level of electrical conductivity between conductors (such as metals) and insulators (such as non-metals). Semiconductors are characterized by their ability to conduct electric current under certain conditions and to exhibit unique electrical properties.
The conductivity of a semiconductor can be modified by factors such as temperature, impurities, and applied electric fields. This property makes semiconductors highly useful in electronic devices and technology.
Semiconductors are typically crystalline solids composed of elements from groups III and V or II and VI in the periodic table, such as silicon (Si) and germanium (Ge). They can also be compounds, such as gallium arsenide (GaAs) or indium antimonide (InSb).
Que 8: Define: Conduction band, Valence band and band gap.
Ans: Valence Band : The band of energies occupied by the valence electrons is called as valence band. This is the highest occupied band below which all the lower bands are fully occupied. The electrons in the outermost orbit of an atom are known as valence electron.
Conduction Band : The band, above the valence band, occupied by conduction electrons is known as conduction band. This is the uppermost band and all electrons in the conduction band are free electrons. The conductor band is empty for insulators and partially filled for conductors.
Band or Energy Gap : The gap between the valence band and the conduction band is known as forbidden band or energy gap.
Que 9: What are the types of semiconductor? Explain in detail with necessary diagrams and examples.
Ans: Semiconductors are divided into two types, intrinsic semiconductors, and extrinsic semiconductors.
Intrinsic semiconductors:
The pure semiconductors (elements of 14 or IV) Group of periodic table) are called Intrinsic Semiconductor.
Practically pure semiconductors free from impurities are not possible. However if the impurities is less than 1 in part of semiconductor it can be treated as intrinsic.
Si and Ge are two common example of intrinsic type of semiconductor. The valency of these atoms is four. Thus, in a crystal each atom shares its four electrons with its immediate neighbors on a one to one bias, so that each atom is involved in four covalent bonds.
At 0 K, all the electrons are bound in covalent bonding and so the crystal is a perfect insulator. As the temperature of the crystal increases, electrons will get free due to thermal energy. When an electron escapes from a bond it leaves behind a vacancy in the lattice. This vacancy is termed as a ‘hole’. Thus when covalent bond is broken due to thermal energy, an electron-hole pair is created.
A bond where Hole created is now becomes unstable and hence an electron will occupy this vacancy from another neighboring bond. But again this bond becomes unstable due to vacancy of electron.
Red curve: Path of movement of electron
Pink curve: Path of movement of Hole
Extrinsic Semiconductor :
The conductivity of the intrinsic semiconductor is very low. To increase the conductivity of an intrinsic semiconductor, a suitable impurity atom is added with the intrinsic semiconductor. The process of mixing suitable impurity with an intrinsic semiconductor is done by doping method.
Thus the extrinsic semiconductor is defined as Intrinsic semiconductors + impurity atom
Type of the extrinsic semiconductor
- P-Type Extrinsic semiconductor
- N-Type Extrinsic semiconductor
Que 10: Mention a few differences between Intrinsic and Extrinsic semiconductors.
Ans:
| Intrinsic Semiconductor | Extrinsic Semiconductor |
|---|---|
| The semiconductor in its pure form is known as intrinsic semiconductor. | When a impurity is added to an intrinsic semiconductor, then the resulting semiconductor is known as extrinsic semiconductor. |
| In case of intrinsic semiconductor, there is no doping or addition of impurity. | In an extrinsic semiconductor, the doping is performed, i.e. a small amount of impurity is added in the pure semiconductor. |
| The electrical conductivity of intrinsic semiconductors is low. | The extrinsic semiconductors have high electrical conductivity. |
| The intrinsic semiconductor does not conduct at 0 Kelvin temperature. | The extrinsic semiconductor conducts at 0 Kelvin temperature. |
| There is no classification of intrinsic semiconductor. | Based on the impurity added, the extrinsic semiconductors are of two types viz. P-type semiconductor and N-type semiconductor. |
| The crystalline forms of pure silicon and germanium are the examples of intrinsic semiconductors. | The examples of extrinsic semiconductors are pure silicon and germanium doped with chemical impurities like As, P, Bi, Sb, In, B, Al, etc. |
Que 11: Explain band theory of solids in detail.
Ans: In crystals, the value of a lattice constant is of order of linear dimensions of atoms (~ 1Å). Obviously at such a short separation between various neighboring atoms, electrons in an atom can not only be subjected to the Coulomb force of the nucleus of this atom but also by Coulomb forces due to nuclei and electrons of the neighboring atoms. In fact it is this interaction which results in the bonding between various atoms which leads to the formations of crystals.
Consider an isolated hydrogen atom. Assume that two such atoms are brought together.
Let u1 and u2 denote the electronic wave functions for the two atoms when they are far apart and are not influenced by one another.
As the separation between the atoms is decreased, the wave function u1 and u2overlap and the resultant electronic wave function due to the two nuclei may be either u1 + u2 or u1 – u2.
For the wave function u1 + u2 , the electron has a finite probability of existing midway between the two nuclei. For the wave function u1 – u2 , the probability density is zero midway. Thus there is a difference in energy between the states (u1 + u2 ) and (u1 – u2 ).
This means that as the two atoms are brought close together, each energy state splits into two distinct energy states. If N no. of atoms are brought together, each energy state splits into N distinct energy states.
When N is large, the separation between these energy states is small and they may be thought to produce a quasi-continuous band.
That is each energy level may be considered to split into a band of energy levels. The width of a band depends on the strength of interaction and overlap between the neighboring atoms.
Que 12: Define terms: (i) Density of States (ii) Fermi level (iii) Occupation Probability
Ans: Density of energy – The density of states is a measure of the number of energy states available per unit energy range in a material’s electronic band structure.
Fermi level – The highest energy level that an electron can occupy at the absolute zero temperature is known as the Fermi Level. The Fermi level lies between the valence band and conduction band because at absolute zero temperature.
The occupation probability indicates the probability that a state with energy is occupied at temperature . At absolute zero the probability that the state with energy is occupied is exactly 50%: .
Que 13: Derive equation for concentration of electrons of effective mass ‘m’ in a conduction band of an intrinsic semiconductor.
Ans:
Que 14: Derive equation for concentration of holes in a valence band of an intrinsic semiconductor.
Ans:
Numerical:
Que 15: Calculate the energy difference between the ground state and the first excited state for an electron in a one-dimensional box of length 10-8 cm. (Mass of electron is 9.1 x 10-31 kg and h = 6.63 x 10-34 J.sec.)
Ans:
$$E_{n} = \frac{n ^{2} h^{2}}{8ma^{2}}$$
h = 6.62 × 10–34 Js, m = 9.1 × 10–31 kg and a = 10–8 × 10-2 m
En = n2 ×(6.62×10-34)2/(8×9.1×10-31×(10-10)2 )
= n2 × 0.6019 × 10-17 J
=0.6019 × 10-17 / (1.6 × 10-19) eV
En = 37.62 n2 eV
For ground state (n=1), E1 =37.62 eV
For exited state (n=2), E2 =150.48 eV
E2 – E1 = 112.86 eV
Que 16: Calculate the number of photons emitted by a 100 watt sodium lamp. The wavelength of emitted light is 5893 Å.
Ans: λ = 5893 Å = 5893 * 10-10 m
Total energy emitted per sec =100
E = hv = hc /λ = 6.62 * 10-34 3*108 / 5893 * 10-10
E = 3.370 * 10-19 J
the total number of photons emitted per sec
N = Total energy emitted per sec / energy of one photon
N = 100/3.370 * 10-19
= 2.967 * 1020 per sec.
Que 17: Calculate the energy in eV for a photon of wavelength 0.1 x 10-9 m. What is the momentum of this photon?
Ans: λ = 0.1×10-9 m, E = ?, p = ?
E = hv = hc/λ = 6.62×10-34 3× 108 / 0.1 × 10-9
E = 1.98 × 10-17 J = 124.25 eV
Momentum of the photon is
p = h/λ = 6.62 × 10-34 / 0.1 × 10-9
p = 6.62 × 10-24 kgms-1
Que 18: Find the energy of an electron moving in one dimension in an infinitely high potential box of width 0.1 nm. (Take n = 1 for least energy of particle).
Ans:$$E_{n} = \frac{n ^{2} h^{2}}{8ma^{2}}$$
when the particle is in the least energy state (n = 1), the energy
$$E_{1} = \frac{h^{2}}{8ma^{2}}$$
h = 6.62×10–34 Js, m = 9.1×10–31 kg and a = 1× 10–10 m
E1 = (6.62×10–34 )2 / (8×9.1 × 10–31 ×(1×10–10 )2 )
E1 = 0.6019 × 10-17 J
= 0.6019 × 10-17 / (1.6 × 10-19) eV
E1 = 37.62 eV
Question 12 ka answer de do
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