1 Theory Theory of of the the electron electron The electron (cathode rays) were “scientifically discovered” by J. J. Thomson in 1896 at Cavendish Labs in Cambridge, UK. There were some very brave assertions by Thomson and his group one of which later proved to be incorrect. These were: 1. Cathode rays are charged particles (which he called 'corpuscles'). 2. These corpuscles are constituents of the atom. 3. These corpuscles are the only constituents of the atom. Later on, in 1911, a brilliant experimentalist, Robert Millikan determined the charge of the electron with his famous “oil drop” experiment. After many attempts, he observed that the force due to the external field applied to each droplet was always divisible by 1.602 x 10 -19 . This was the charge of one electron in Coulombs. Remember: F = E x q, in Millikan’s experiment, he knew E and F. F was –m x g (gravitational force acting on the droplet).
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1
TheoryTheory of of thethe electronelectron
The electron (cathode rays) were “scientifically discovered” by J. J.
Thomson in 1896 at Cavendish Labs in Cambridge, UK. There were
some very brave assertions by Thomson and his group one of which later
proved to be incorrect.
These were:
1. Cathode rays are charged particles (which he called 'corpuscles').
2. These corpuscles are constituents of the atom.
3. These corpuscles are the only constituents of the atom.
Later on, in 1911, a brilliant experimentalist, Robert Millikan determined the
charge of the electron with his famous “oil drop” experiment. After many
attempts, he observed that the force due to the external field applied to each
droplet was always divisible by 1.602 x 10-19. This was the charge of one
electron in Coulombs.
Remember: F = E x q, in Millikan’s experiment, he knew E and F. F was
–m x g (gravitational force acting on the droplet).
radiation, electrons are ejected at certain energies
in the “photoelectric effect” experiments.
DespiteDespite a a continuouscontinuous variationvariation of of incomingincoming
radiationradiation, , electronselectrons areare ejectedejected at at certaincertain energiesenergies
in in thethe ““photoelectricphotoelectric effecteffect”” experimentsexperiments..
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Time Time toto talk talk aboutabout thethe birthbirth of of quantumquantum physicsphysics conceptsconcepts
BlackBlack body body radiationradiation
HydrogenHydrogen emissionemission spectraspectra
EveryEvery energyenergy--exchangeexchange
happenshappens in in discretediscrete
amountsamounts !!
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UnderstandingUnderstanding thethe blackblack body body radiationradiation ((SoonSoon it it willwill be be appliedapplied toto electronselectrons!)!)
Black body radiation was the earliest puzzle to be solved. Max Planck made a
ad-hoc (full of assumptions-that he did not know whether they were correct or
not) attempt to explain it.
Nu
mb
er
Nu
mb
er
of
of m
od
es
mo
des
ForFor higherhigher frequenciesfrequencies, , moremore curvescurves can be fit can be fit withwith thethe constraintconstraint thatthat thethe
wavewave functionfunction willwill becomebecome zerozero at at thethe wallwall ((BoundaryBoundary conditioncondition).).
““If the mode is of shorter wavelength, there are more ways you caIf the mode is of shorter wavelength, there are more ways you can fit it into the cavity to meet that n fit it into the cavity to meet that
condition. Careful analysis by Rayleigh and Jeans showed that thcondition. Careful analysis by Rayleigh and Jeans showed that the number of modes was proportional to e number of modes was proportional to
the frequency squared.the frequency squared.”” ((http://hyperphysics.phyhttp://hyperphysics.phy--astr.gsu.edu/hbaseastr.gsu.edu/hbase))
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Energ
yE
nerg
yof
of ra
dia
tion
radia
tion
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WhatWhat is a is a ““standingstanding wavewave””??
“…a wave that neither goes left nor right (in 1D)”
A wave whose ends are fixed
The wave equation in 3D
General solution
When the general solution
is substituted into the wave
equation.
Simplify and you end up
with this
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MaxMax Planck Planck assumedassumed thatthat: : ThereThere areare oscillatorsoscillators on on thethe wallswalls of of thethe enclosureenclosure (inside (inside
electromagneticelectromagnetic radiationradiation ((justjust likelike thethe electronelectron oscillatingoscillating upup andand downdown on a on a
antennaantenna))
TheThe electricelectric fieldfield andand magneticmagnetic fieldfield has has toto be be zerozero at at thethe wallwall ((otherwiseotherwise wewe getget
chargingcharging on on thethe wallswalls of of thethe furnacesfurnaces –– whowho getsgets an an electricelectric shockshock whenwhen touchingtouching
a hot a hot surfacesurface?)?)
RememberRemember: : TheThe shortershorter thethe wavelengthwavelength, , thethe moremore numbernumber of of curvescurves couldcould be be
producedproduced toto fit inside fit inside thethe cubecube. . TheseThese curvescurves areare eacheach calledcalled ““modesmodes””. .
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MaxMax Planck Planck modificationmodification
((oror correctioncorrection))
AccordingAccording toto RayleighRayleigh andand JeansJeans, , thethe numbernumber of of
modesmodes possiblepossible toto fit inside fit inside thethe cubecube goesgoes toto infinityinfinity
ElectronicElectronic--MagneticMagnetic--OpticalOptical PropertiesProperties areare allall aboutabout thethe behaviorbehavior of of electronselectrons in in
solidssolids..
A A fewfew examplesexamples::
--VeryVery weaklyweakly boundbound electronselectrons withwith ““availableavailable densitydensity of of statesstates ((emptyempty parkingparking lot)lot)””: :
ConductorsConductors
--UnpairedUnpaired electronselectrons in in termsterms of of spinsspins in in thethe outerouter shellsshells::
MagnetismMagnetism
--ElectronsElectrons in in ““bandsbands”” thatthat cannotcannot movemove anywhereanywhere ((fullfull parkingparking lot) but lot) but somesome can can
jumpjump toto thethe nextnext availableavailable//allowedallowed bandband andand thenthen theythey havehave plentyplenty of of statesstates toto hop hop