Quantum Numbers

Quantum numbers describe values of conserved quantities in the dynamics of a quantum system. In the case of quantum numbers of electrons, they can be defined as "The sets of numerical values which give acceptable solutions to theSchrödinger wave equation for the Hydrogen atom". Perhaps the most important aspect of quantum mechanics is thequantization of observable quantities, since quantum numbers are discrete sets of integers or half-integers, although they could approach infinity in some cases. This is distinguished from classical mechanics where the values can range continuously. Quantum numbers often describe specifically the energy levels of electrons in atoms, but other possibilities include angular momentum, spin, etc. Any quantum system can have one or more quantum numbers; it is thus difficult to list all possible quantum numbers.

There are four quantum numbers which can describe the electron completely.

• Principal quantum number (n)
• Azimuthal quantum number (ℓ)
• Magnetic quantum number (m)
• Spin quantum number (s)

The principal quantum number (n) describes the electron shell, or energy level, of an atom. The value of n ranges from 1 to the shell containing the outermost electron of that atom.

The azimuthal quantum number (ℓ) (also known as the angular quantum number or orbital quantum number) describes the subshell, and gives the magnitude of the orbital angular momentum.

The magnetic quantum number (m_ℓ) describes the specific orbital (or "cloud") within that subshell, and yields the projection of the orbital angular momentum along a specified axis.

The spin projection quantum number (m_s) describes the spin (intrinsic angular momentum) of the electron within that orbital, and gives the projection of the spin angular momentum S along the specified axis. An electron has spin s = ½, consequently m_s will be ±½, corresponding with "spin" and "opposite spin." Each electron in any individual orbital must have different spins because of the Pauli exclusion principle, therefore an orbital never contains more than two electrons.

Name	Symbol	Orbital meaning	Range of values	Value examples
principal quantum number	n	shell	1 ≤ n	n = 1, 2, 3, …
azimuthal quantum number (angular momentum)	ℓ	subshell (s orbital is listed as 0, p orbital as 1 etc.)	0 ≤ ℓ ≤ n − 1	for n = 3: ℓ = 0, 1, 2 (s, p, d)
magnetic quantum number, (projection ofangular momentum)	mℓ	energy shift (orientation of the subshell's shape)	−ℓ ≤ mℓ ≤ ℓ	for ℓ = 2: mℓ = −2, −1, 0, 1, 2
spin projection quantum number	ms	spin of the electron (−½ = "spin down", ½ = "spin up")	−s ≤ ms ≤ s	for an electron s = ½, so ms = −½, ½

Source: http://en.wikipedia.org/wiki/Quantum_number

Another recommended reading: http://skullsinthestars.com/2008/05/27/the-gallery-of-failed-atomic-models-1903-1913/

first-ever beam of antihydrogen atoms

CERN announced that its ASACUSA experiment has produced the world's first-ever beam of antihydrogen atoms. Such beams will make possible a couple of tests that seek to answer one of the biggest questions in physics: Why is there more matter than antimatter?

"The ASACUSA experiment at CERN has succeeded for the first time in producing a beam of antihydrogen atoms. In a paper published today in Nature Communications, the ASACUSA collaboration reports the unambiguous detection of 80 antihydrogen atoms 2.7 metres downstream of their production, where the perturbing influence of the magnetic fields used initially to produce the antiatoms is small. This result is a significant step towards precise hyperfine spectroscopy of antihydrogen atoms." in CERN Press Office

The evolution concept of the atom

Credit: discover.physics and eufisica

News in NanoCarbon TeK

This week in PhysOrg the recent news in nanocarbon technology:

'Unzipped' carbon  nanotubes  could  help  energize  fuel  cells,  batteries

This drawing shows the damaged outer wall of a carbon nanotube with nanosized graphene pieces (white patches), which facilitate the formation of catalytic sites made of iron (yellow) and nitrogen (red) atoms. The catalyst reduces oxygen to water. Credit: Guosong Hong

Multi-walled carbon nanotubes riddled with defects and impurities on the outside could replace some of the expensive platinum catalysts used in fuel cells and metal-air batteries, according to scientists at Stanford University. Their findings are published in the May 27 online edition of the journal Nature Nanotechnology. (here)

Scientists  take  steps  toward  creating  artificial  graphene

(Phys.org) -- Researchers first observed graphene in 2004 by extracting the single-atom-thick sheets of carbon from bulk graphite. While graphene’s electrical and optical properties have proven to have extraordinary potential for many applications, creating atomically precise structures out of graphene remains challenging. In an effort to improve graphene’s usability, scientists have been searching for a way to fabricate artificial graphene, which could serve as a helpful structure where devices can be easily tested before their implementation with natural graphene. Now in a new study, scientists have identified all the main criteria required to make artificial graphene, which could provide a guide for experimentally realizing the material. (here)

Researchers  find  new  properties  of  the  carbon  material  graphene

Graphene has caused a lot of excitement among scientists since the extremely strong and thin carbon material was discovered in 2004. Just one atom thick, the honeycomb-shaped material has several remarkable properties combining mechanical toughness with superior electrical and thermal conductivity. (here)

Magnifying the Universe

Magnifying the Universe is an interactive infographic that illustrates the scale of over 100 items. From galaxies to insects, nebulae and stars to molecules and atoms. And more...

Click to view in full screen and start using it:

Copyright 2012. Magnifying the Universe by Number Sleuth.

A new technique lets see atomic structure in 3-D

Jianwei Miao and colleagues have developed an electron tomography method to image the 3-D structure of a gold nanoparticle at a resolution of 2.4 angstroms. Individual atoms are observed in some regions of the particle and several grains are identified in three dimensions. In the figure, the four three-dimensional grains (green and gold; blue and red) form two pairs of twin boundaries inside the nanoparticle. Credit: Jianwei Miao/UCLA Physics & Astronomy, CNSI 

(PhysOrg.com) -- UCLA researchers are now able to peer deep within the world's tiniest structures to create three-dimensional images of individual atoms and their positions. Their research, published March 22 in the journal Nature, presents a new method for directly measuring the atomic structure of nanomaterials.

Don't think atomic nucleus' as static

(PhysOrg.com) -- When most of us think of an atom, we think of tiny electrons whizzing around a stationary, dense nucleus composed of protons and neutrons, collectively known as nucleons. A collaboration between the U.S. Department of Energy's Argonne and Thomas Jefferson National Laboratories has demonstrated just how different reality is from our simple picture, showing that a quarter of the nucleons in a dense nucleus exceed 25 percent of the speed of light, turning the picture of a static nucleus on its head.


Watch this video from fairlight tuitition with topics about the atom:

Evidence of rare hypernucleus

A view of one of the three events found by FINUDA: a schematic frontal view of the apparatus is shown, and the two blue lines represent the two 'pi' mesons moving along opposite bent trajectories in the magnetic field of the apparatus. Image credit: FINUDA collaboration

(PhysOrg.com) -- Physicists in Italy have discovered the first evidence of a rare nucleus that doesn’t exist in nature and lives for just 10^-10 seconds before decaying. It’s a type of hypernucleus that, like all nuclei, contains an assortment of neutrons and protons. But unlike ordinary nuclei, hypernuclei also contain at least one hyperon, a particle that consists of three quarks, including at least one strange quark. Hypernuclei are thought to form the core of strange matter that may exist in distant parts of the universe, and could also allow physicists to probe the inside of the nucleus.

The particular hypernucleus investigated here, called "hydrogen six Lambda" (⁶_ΛH).

Ohm's law in atomic scale

Atomic wire made of phosphorus. It links to silicon atoms.
Credit: Physics World

Ohm's Law

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship:

 where I is the current through the conductor in units of amperes, V is the potential difference measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current.

The law was named after the German physicist Georg Ohm, who, in a treatise published in 1827, described measurements of applied voltage and current through simple electrical circuits containing various lengths of wire. He presented a slightly more complex equation than the one above to explain his experimental results. The above equation is the modern form of Ohm's law.

In physics, the term Ohm's law is also used to refer to various generalizations of the law originally formulated by Ohm. The simplest example of this is:

where J is the current density at a given location in a resistive material, E is the electric field at that location, and σ is a material dependent parameter called the conductivity. This reformulation of Ohm's law is due to Gustav Kirchhoff.

Microscopic origins of Ohm's law

The dependence of the current density on the applied electric field is essentially quantum mechanical in nature; (see Classical and quantum conductivity.) A qualitative description leading to Ohm's law can be based upon classical mechanics using the Drude model developed by Paul Drude in 1900.

The Drude model treats electrons (or other charge carriers) like pinballs bouncing between the ions that make up the structure of the material. (read more in Wikipedia).

An atomic scale experiment results 

"A new technique for embedding atomic-scale wires within crystals of silicon has revealed that Ohm's law can hold true for wires just four atoms thick and one atom tall. The result comes as a surprise because conventional wisdom suggests that quantum effects should cause large deviations from Ohm's law for such tiny wires. Paradoxically, the researchers hope the finding will aid the development of quantum computers."

in Physics World (click to read entire article)

A team of Arizona State University created a channel in the silicon by removing layers of silicon atoms, by using the tip of a scanning probe microscope. The surface was then exposed to phosphorus gas, followed by the deposition of silicon atoms. The result was a chain of phosphorus atoms embedded inside a silicon crystal – an atomic wire. The team found that the resistivity of those wires was constant. That means the resistance of such a wire is proportional to its length and inversely proportional to its area, just as we seen in Ohm's law.

Implications

The discovery has several implications, including:

• For engineers it could provide a roadmap to future nanoscale computational devices where atomic sizes are at the end of Moore's law. The theory shows that a single dense row of phosphorus atoms embedded in silicon will be the ultimate limit of downscaling.

• For computer scientists, it places donor-atom based silicon quantum computing closer to realization.

• And for physicists, the results show that Ohm's Law, which demonstrates the relationship between electrical current, resistance and voltage, continues to apply all the way down to an atomic-scale wire.

in ScienceDaily

Beryllium in primordial Big Bang

Amplify’d from www.physorg.com

Credit: wikimedia (PhysOrg.com) -- Some chemical elements appear much more abundantly in nature than others, which is partly due to how the elements originally formed. Scientists know that the light elements (hydrogen, deuterium, helium, and traces of lithium) were produced by fusion in the early Universe. Today, lithium, beryllium, and boron are constantly being produced in cosmic rays, while the heavier elements (up to iron) are formed by fusion in stars. Elements heavier than iron are formed by supernovae. Read more at www.physorg.com

See this Amp at http://bit.ly/fqeLZE

PhysicsCentral: Buzz Blog

PhysicsCentral: Buzz Blog

WASHINGTON — For the first time, physicists have photographed the structure of an atom down to its electrons.

The pictures, soon to be published in the journal Physical Review B, show the detailed images of a single carbon atom's electron cloud, taken by Ukrainian researchers at the Kharkov Institute for Physics and Technology in Kharkov, Ukraine.

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