# 3.37 Sspd_chapter 1_part 14_bosons , fermions and physics of laser  (Page 2/3)

(1/3)/(1/4)= (4/3) = 1.333

In the above example distinguishable coins are Fermions and indistinguishable are Bosons.

1.14.2. THE SCATTERING OF DISTINGHUISHABLE AND INDISTINGHUISH ABLE PARTICLES.

In Figure(1.78) the scattering system of two indistinguishable particles is shown. The indistinguishable particles are alpha particles.

Figure 1.78. Scattering of two indistinguishable particles.

We clearly see that an alpha particle is detected at a scattering angle θ 1 irrespective of the fact that the particle may be scattered at θ 1 or at θ 2 . This is because the alpha particles are indistinguishable. Hence

If probability amplitude of detection at θ 1 is ψ(θ 1 )

And probability amplitude of detection at θ 2 is ψ(θ 2 ),

Then total probability density of detection of alpha particles at θ 1 is

| ψ(θ 1 ) + ψ(θ 2 )| 2 …………………………………………………………. 1.138

In the same scattering set up if α- α pair is replaced by α-O 2 pair the probability density of detection of α particles at θ 1 is

| ψ(θ 1 ) - ψ(θ 2 )| 2 ……………………………………………………… 1.139

This is because the scattering at θ 2 gives the detection of O 2 which is completely distinguishable from the alpha particle.

Eq.(1.138) and Eq.(1.139) bring out the fundamental difference between bosons and fermions.

1.14.2. SCATTERING OF N PHOTONS LOCALIZED IN THE SAME SPATIAL CELL.

In one elemental phase cell (meaning by at the same energy level and in the same spatial space) only two fermions of opposite spin are accommodated. If a third fermion pushes itself in the cell it will be repulsed. Therefore we say fermions are segregative.

But in an elemental phase cell any number of photons can aggregate. As the number increases the tendency to aggregate increases. A quantitative measure of aggregation tendency comes out while theoretically analyzing Black body Radiation.

Suppose in a cavity the emission and absorption of photons are in equilibrium then the average energy at a given frequency is shown to be:

<E>= ћω/[Exp(ћω/(kT)) -1] ………………………………………….. 1.140

Planck assumed that every black body radiator is composed of harmonic oscillators which oscillate at fundamental and harmonic frequencies only

that is at ω, 2 ω, 3 ω, 4 ω….. and their discrete energies are ћω , 2 ћω, 3 ћω, 4 ћω..

If total number of oscillators is N 0 0 and if we assume that they are in energy equilibrium then from Maxwell – Boltzmann statistics:

If N 0 is the number of oscillators at 0 energy then

N 0 / N 0 0 = Exp(-0/kT) = 1

N 1 is the number of oscillators at ћω then

N 1 / N 0 0 = Exp[-ћω/kT]

N N is the number of oscillators at nћω then

N N / N 0 0 = Exp[-N ћω/kT] ………………………………………………………… 1.141

Equation(1.141) have been set up according to Maxwell-Boltzmann Statistics which states that at temperature T Kelvin, probability of existence at energy level E is :

P(E) = Exp(-E/kT)…………………………………………………………… 1.142

So the average energy (per oscillator) = total energy/ total number of oscillators

<E>= E total /N tot

= [(0× N 0 ) + (ћω× N 1 )+ (2ћω× N 1 )+ (3ћω× N 3 )+…..]/[ N 0 +N 1 + N 2 + N 3 +..]……………………………………………………………………………………………….. 1.143

Dividing Numerator and Denominator by N tot = N 0 0 ,

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
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