5559501 Project on Atomic Structure

8/3/2019 5559501 Project on Atomic Structure

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DISCOVERY OF ELECTRONS

Hundred years ago, amidst glowing glasstubes and the hum of electricity, the Britishphysicist J.J Thomson. was venturing intothe interior of the atom. At the CavendishLaboratory at Cambridge University,Thomson was experimenting with currentsof electricity inside empty glass tubes. He

was investigating a long-standing puzzleknown as "cathode rays." His experimentsprompted him to make a bold proposal:these mysterious rays are streams ofparticles much smaller than atoms, they arein fact minuscule pieces of atoms. He calledthese particles "corpuscles," and suggestedthat they might make up all of the matter inatoms. It was startling to imagine a particleresiding inside the atom--most peoplethought that the atom was indivisible, themost fundamental unit of matter.

Cathode ray tube

J.J Thomson


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During the 1880s and 90s scientists searchedcathode rays for the carrier of the electricalproperties in matter. Their work culminated in thediscovery by English physicist J.J. Thomson of theelectron in 1897. The existence of the electron

showed that the 2,000-year-old conception of theatom as a homogeneous particle was wrong andthat in fact the atom has a complex structure.

Cathode-ray studies began in 1854 when HeinrichGeissler, a glassblower and technical assistant tothe German physicist Julius Plcker, improved thevacuum tube. Plcker discovered cathode rays in1858 by sealing two electrodes inside the tube,evacuating the air, and forcing electric current

between the electrodes. He found a green glow onthe wall of his glass tube and attributed it to raysemanating from the cathode. In 1869, with bettervacuums, Plckers pupil Johann W. Hittorfsaw ashadow cast by an object placed in front of thecathode. The shadow proved that the cathode raysoriginated from the cathode. The English physicistand chemist William Crookes investigated cathoderays in 1879 and f

ound that they were bent by amagnetic field; the direction of deflection

suggested that they were negatively chargedparticles. As the luminescence did not depend onwhat gas had been in the vacuum or what metal theelectrodes were made of, he surmised that the rayswere a property of the electric current itself. As aresult of Crookess work, cathode rays were widelystudied, and the tubes came to be called Crookestubes


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Anode rays (orCanal rays) wereobserved in experiments by a Germanscientist, Eugen Goldstein, in 1886.Goldstein used

a gas discharge tubewhich had a perforated cathode. A"ray" is produced in the holes (canals)in the cathode and travels in adirection opposite to the "cathoderays," which are streams of

electrons.Goldstein called these positive rays"Kanalstrahlen" - canal rays because itlooks like they are passing through acanal. In 1907 a study of how this "ray"was deflected in a magnetic field,revealed that the parti

cles making up

the ray were not all the same mass.The lightest, formed when there was alittle hydrogen in the tube, wascalculated to be 1837 times asmassive as an electron. They wereprotons

CANAL RAYS


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Discovery of the Neutron

It is remarkable that the neutron was notdiscovered until 1932 when JamesChadwick used scattering data tocalculate the mass of this neutral particle.Since the time ofRutherford it had beenknown that the atomic mass number A ofnuclei is a bit more than twice the atomic

number Z for most atoms and thatessentially all the mass of the atom isconcentrated in the relatively tinynucleus. As of about 1930 it waspresumed that the fundamental particleswere protons and electrons, but thatrequired that somehow a number of

electrons were bound in the nucleus topartially cancel the charge of A protons.But by this time it was known from theuncertainty principle and from "particle-in-a-box" type confinement calculationsthat there just wasn't enough energyavailable to contain electrons in thenucleus.


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J. J. Thomson considered that thestructure of an atom is somethinglike a raisin bread, so that hisatomic model is sometimes calledthe raisin bread model. Heassumed that the basic body of anatom is a spherical objectcontaining N electrons confined inhomogeneous jellylike but relativelymassive positive charge distributionwhose total charge cancels that ofthe Nelectrons. The schematicdrawing of this model is shown inthe following figure. Thomson'smodel is sometimes dubbed aplum pudding model.

J. J. Thomson's raisin bread model

(plum pudding model)


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In the years 1909-1911 Ernest Ruthefordandhis students - Hans Geiger(1882-1945) andErnest Marsden conducted someexperiments to search the problem of alphaparticles scattering by the thin gold-leaf.Rutheford knew that the particles contain the

2e charge. The experiment caused thecreation of the new model of atom - the"planetary" model.

Rutheford suggested to hit the gold-leaf(picture no. 1) with fast alpha particles fromthe source 214Po. (The source R was in thelead lining F). The particles felt from the

source on the gold-leaf E and were observedby the microscope M. The whole experimentwas in the metal lining A and was coveredwith the glass plate P. The instrument wasattached to the footing B. The gold leaf wasabout 5*10-7 meter thick. The scientist knewthat reckoning the scattering angle could saymuch about the structure of atoms of the

gold-leaf.

RUTHERFORDS ALPHA

SCATTERING EXPERIMENT


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Rutheford made a theoretical analysis ofangles of scattering in accordance withThomson's theory of atom and in accordancewith his own theory. He assumed that atomconsisted of positive charged nucleus andnegative charged electrons circling aroundthe nucleus. Then his theoretic calculations

he compared with the experiment result.Alpha particles going through atom createdin accordance with the "plum cake" modelwouldn't be strong abberated because theelectric field in that atom wouldn't be strong.In the model created by Rutheford the field ismuch stronger near to the nucleus, so someof alpha particles are much more abberated.The other going in the far distance to thenucleus are almost not at all abberated. Theprobability that any alpha particle will hit thenucleus is small but there is such a chance.


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PLANETARY MODEL OF ATOM BY

BOHR The Bohr Model is probably familar as

the "planetary model" of the atomillustrated in the adjacent figure that,for example, is used as a symbol foratomic energy (a bit of a misnomer,since the energy in "atomic energy" isactually the energy of the nucleus,rather than the entire atom). In theBohr Model the neutrons and protons(symbolized by red and blue balls inthe adjacent image) occupy a densecentral region called the nucleus, andthe electrons orbit the nucleus muchlike planets orbiting the Sun (but theorbits are not confined to a plane as is

approximately true in the SolarSystem). The adjacent image is not toscale since in the realistic case theradius of the nucleus is about 100,000times smaller than the radius of theentire atom, and as far as we can tellelectrons are point particles without aphysical extent

This similarity between a planetarymodel and the Bohr Model of theatom ultimately arises because theattractive gravitational force in asolar system and the attractiveCoulomb (electrical) force betweenthe positively charged nucleus andthe negatively charged electrons inan atom are mathematically of thesame form. (The form is the same,but the intrinsic strength of theCoulomb interaction is much largerthan that of the gravitationalinteraction; in addition, there arepositive and negative electrical

charges so the Coulomb interactioncan be either attractive or repulsive,but gravitation is always attractive inour present Universe.)


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QUANTUM MECHANICAL MODEL According to the Principles ofQuantum Mechanics electrons are

distributed around the nucleus in "probability regions". Theseprobability regions are called "atomic orbitals". According toQuantum Mechanics, these orbitals are mathematically definedand are described by a uniquely different math function for eachelectron in the atom called an "eigen function" and a differentialequation generated by the following equation:

H(eigen function) = Energy ( eigen function)

The H in the above equation stands for a mathematical operator

called the Hamiltonian. We should be familiar with mathoperators since we have been dealing with them since gradeschool. The addition operator has to operate upon two numbersone that appears on its left and the other on its right. Forexample the addition operator operates upon the number 4 and 3and the result of that operation as all knows would be 7. Wehave subtraction, multiplier, division,common log, naturallog,exponentiation,etc. The Hamiltonian operator is kinda likethese but much more complex. The result of the Hamiltonianoperator operating on the eigen function of an electron is to

generate a differential equation. Differential equations often havemore than one root or solution which is not new to those whohave had a first year algebra course where quadratic equationsare studied. However, one property of differential equations thatmight be new to you is the fact that differential equations cannotbe solved exactly. We must use approximation methods toextract any roots out of the equation, and those roots or solutionswill be approximate solutions.


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5559501 Project on Atomic Structure