Topic – 5 Fundamentals of Quantum Theory
Why do we prefer black coloured umbrella during hot days?
Black color umbrella absorbs more heat and it quickly emits the radiation.
A perfect black body is the one which absorbs completely heat radiations of all
wavelengths which fall on it and emits heat radiations of all wavelengths when heated.
Since a perfect black body neither reflects nor transmits any radiation, the absorptive
power of a perfectly black body is unity
The sky appears blue in colour. Comment
The blue color of the sky is due to Rayleigh scattering. blue sky As light moves through
the atmosphere, most of the longer wavelengths pass straight through. Little of the red,
orange and yellow light is affected by the air.
However, much of the shorter wavelength light is absorbed by the gas molecules. The
absorbed blue light is then radiated in different directions. It gets scattered all around the
sky. Whichever direction you look, some of this scattered blue light reaches you. Since
you see the blue light from everywhere overhead, the sky looks blue.
What is a perfect black body?
A perfect black body is the one which absorbs completely heat radiations of all
wavelengths which fall on it and emits heat radiations of all wavelengths when heated.
Since a perfect black body neither reflects nor transmits any radiation, the absorptive
power of a perfectly black body is unity
Compare classical physics and quantum physics.
Classical
Quantum
It deals with macroscopic particles
It deals with microscopic particles
It is based upon Newton’s laws of motion
It takes into account Heisenberg’s uncertainty
principle and de Broglie concept of dual nature
of matter (particle and wave nature)
It state of the system is defined by Newtonian
It state of the system is defined by wave
law
function.
Explain the concept of matter waves.
de Broglie relations show that the wavelength is inversely proportional to the momentum
of a particle. The Davisson-Germer experiment demonstrated the wave-nature of matter
and completed the theory of wave-particle duality.
Related to Unit – II Quantum Physics
Engineering Physics - I
Topic – 5 Fundamentals of Quantum Theory
Derive an expression for de-broglie wavelength.
(i) de Broglie equated the energy equations of Planck (wave) and Einstein (particle).
For a wave of frequency ν, the energy associated with each photon
is given by Planck’s relation, E = hν ...(1)
where h is Planck’s constant. According to Einstein’s mass energy relation, a mass
m is equivalent to energy, E = mc2 ...(2)
where c is the velocity of light. If, h ν = mc2
∴ hc / λ = mc2 (or) λ = h / mc ...(3)
(since ν = c / λ)
For a particle moving with a velocity v , if c = v
from equation (3)
λ = h / mv = h/ p ...(4)
where p = mv
the momentum of the particle. These hypothetical matter waves will have appreciable
wavelength only for very light particles.
(ii) de Broglie wavelength of an electron
When an electron of mass m and charge e is accelerated through a potential difference
V , then the energy eV is equal to kinetic energy of the electron.
1
2eV
mv 2 = eV (or) v = √
2
m
h
h
h
λ=
=
=
mv
2 e V √2 m e V
m√ m
Discus wave mechanical concept of atom
According to de Broglie’s hypothesis, an electron of
mass m
In motion with a velocity v is associated with a wave whose
wavelength λ
is given by λ = h / mv...(1) where h is Planck’s constant. On
the basis of de Broglie’s
hypothesis, an atom model was proposed in which the
stationary orbits of Bohr’s model were retained, but with the
difference that electron in various orbits behaves as a wave.
It was suggested that stationary orbits are those in which
orbital circumference (2π r) is an integral multiple of de
Broglie wavelength λ,
i.e., stationary orbits for an electron are those which contain the
complete waves of electron. Thus, 2 π r = n λ ...(2)
Related to Unit – II Quantum Physics
Engineering Physics - I
Topic – 5 Fundamentals of Quantum Theory
where n = 1, 2, 3 ... and r is the radius of the circular orbit. Substituting equation (1) in equation
(2), 2 π r = n ( h/mv) (or) mv r = nh / 2π ...(3)
From equation (3), it is seen that the total angular momentum of the moving electron is an
integral multiple of h / 2π . Thus, de Broglie’s concept confirms the Bohr’s postulate.
Explain the principle and the process involved in the power generation from
the Solar photo voltaic cells.
A solar photovoltaic cell is an electronic device which directly converts sunlight into electricity.
Light shining on the solar cell produces both a current and a voltage to generate electric power.
This process requires firstly, a material in which the absorption of light raises an electron to a
higher energy state, and secondly, the movement of this higher energy electron from the solar
cell into an external circuit. The electron then dissipates its energy in the external circuit and
returns to the solar cell. A variety of materials and processes can potentially satisfy the
requirements for photovoltaic energy conversion, but in practice nearly all photovoltaic energy
conversion uses semiconductor materials in the form of a p-n junction.
Cross section of a solar photovoltaic cell.
The generation of current in a solar cell, known as the "light-generated current",
involves two key processes. The first process is the absorption of incident photons to
create electron-hole pairs. Electron-hole pairs will be generated in the solar cell
provided that the incident photon has an energy greater than that of the band gap.
Related to Unit – II Quantum Physics
Engineering Physics - I