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Concluding Part 9 describes the wave nature of distinguishable and undistinguishable particles and the resulting Fermi-Dirac distribution and Bose-Einstein distribution respectively. This part describes the multiple fine structure in spectrum is caused due to the removal of degeneracy.

SSPD_Chapter1_Part9_Continued_RELATIVISTIC EFFECTS IN THE HYDROGEN ATOM.

Relativistic Hamiltonian can be fully solved for the Hydrogen atom. Here only the end results are enumerated.

As already seen azimuthial quantum number decides the shape of the subshell corresponding to different l. Now we know from Kepler’s second law [Appendix XXXIII] that a body in elliptical orbit sweeps equal area in equal time. Hence in spherical orbit electron moves with uniform linear velocity all the time but in ellipsoidal orbit apogee velocity is the slowest and perigee velocity is the fastest. If relativistic considerations are made then n fold degeneracy is removed among the different values of l but same n.

Relativistic considerations lead to spin angular momentum of electron. The spin quantum number is s = ±(1/2)ћ.

Table 1.6. Quantum Numbers of an Atomic Electron.

Name Symbol Possible Values Quantity determined
Principal n 1, 2, 3, …. Electron Energy
Azimuthial or Orbital l 0,1, 2, 3, 4,….(n-1);
Magnetic m l -l, -( l -1),…0….( l -1), l Spatial direction of L in presence of Magnetic field
Spin Angular Momentum s -1/2, +1/2 Electron Spin Angular Momentum

From the point of view of quantum numbers, following are the permissible shells and subshells:

Table 1.7. Permissible Shells and Subshells

n l m s subshell Shell
1 0 0 +1/2
-1/2
s K
2 0 0 +1/2
-1/2
s
1 +1 ±1/2
0 ±1/2
-1 ±1/2
p L
3 0 0 +1/2
-1/2
s
1 +1 ±1/2
0 ±1/2
-1 ±1/2
P
2 +2 ±1/2
+1 ±1/2
0 ±1/2
-1 ±1/2
-2 ±1/2
d M

Thus we see that the permissible electrons are subdivided in Major Shells:

K, L, M, N, O, P… where n = 1, 2, 3, 4, 5, 6 ……respectively.

Every Shell has Subshells.

n = 1, K has only s subshell having two electrons differentiated by spin quantum number ±1/2ћ.

n= 2 , L shell has two subshells, s and p subshell. s shell can accommodate at most 2 electrons .

Within L shell, p subshell can accommodate 6 electrons.

Therefore L shell can accommodate 8 electrons altogether.

n=3, M shell has 3 subshells, s. p and d subshells.

s shell can accommodate 2 elecrons,

p shell can accommodate 6 electrons.

d subshell can accommodate at most 10 electrons.

Therefore M shell can accommodate 18 electrons altogether.

Accordingly nth shell can accommodate 2n 2 electrons at most and these 2n 2 electrons are subdivided in s, p, d, f, subshells.

As seen from Table(1.7), no two electrons have the same set of four quantum numbers. This is known as Pauli-Exclusion Principle [Appendix XXXIV] .

SSPD_Chapter 1_Part 9_conclusions_1.8.2_FAR REACHING IMPLICATIONS OF THE REMOVAL OF DEGENERACY.

In Chapter 1_Part 7_Sec(1.6.3.) we had derived the formula for determining the energy of the electron in shell having n principal quantum number. According to Eq.(1.35):

E n = -13.6eV/n 2

According to this formula 2n 2 electrons at n quantum number will all have the same energy. This implies that all the n 2 electrons are at the same energy level. If this was to be true then we would say that all n 2 electrons are in a degenerate state but in fact this is not true. If relativistic considerations and spin considerations are applied then the degeneracy is removed. This has far reaching consequences in terms of the type of particles we are considering.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
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
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
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
Brian Reply
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?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
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 ?
Bob Reply
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?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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Source:  OpenStax, Solid state physics and devices-the harbinger of third wave of civilization. OpenStax CNX. Sep 15, 2014 Download for free at http://legacy.cnx.org/content/col11170/1.89
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