as physics revision - only sdf

8/6/2019 As Physics Revision - Only SDF

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Unit 1

Constituents of the atom

Theres a nucleus containing protons and neutrons. The particles inside nucleus are callednucleons. Particles orbiting this core are the electrons.

Charge Charge/C Mass/u

Proton +1 1.6 X 10-19

1.00728

Neutron 0 0 0

Electron -1 -1.6 X 10-19

5.5 X 10-4

(

Proton Number = Atomic Number, in neutral atom n of electrons = n of protons. Protonnumber tells you lot about its chemical properties. It has symbol Z.

Nucleon Number = Mass number. The mass number A is total number of nucleons. All atoms of the same element have the same number of protons in the nucleus. The number of nucleons: N = A Z An Isotope An atom with the same number of protons but different number of neutrons

Stable and Unstable Nuclei Info

Unstable nuclei may be radioactive and decay to make themselves stable. Among the light nuclei (Z20) have more neutrons than protons. The ratio reaches about 1.5 by lead-

208

Nuclides which lie above the stability belt are likely to decay via emission, which convertsa neutron to a proton

Nuclides which lie below the stability belt are likely to decay via emission, which convertsa proton to a neutron

When Z>60, nuclides below stability belt can also decay by emitting an particle. All nuclides with Z>83 are unstable and those that occur in nature decay via or -

particle emission.


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2 |

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Howeve # $ % & e' ( ) 0

e# of nuc 1 eons that contribute to attractive force on that proton doesnt

change 2 This arises b/c theresidual strong force decaysextre ) ely rapidly with distance$ and

thereforeacts (more or less 3 only between adjacent nucleons2

To restore the balance4 more neutrons are needed. The neutrons4 which interact withprotons and other neutrons only through the residual strong force4 increase the average

separation between protons and so reduce theelectrostatic repulsive forces between them.

The Mysteries of Decay

decayelectrons were found to havecontinuousenergy distribution ranging from zero upto a certain max. value. It wasexpected that they5 like particles5 should carry away a

definite amount ofenergy almost all of theenergy difference between initial and final

states of nucleus.

By1930 two leading physicists held opposing views as to explanation:o Bohr went as far assuggesting that perhaps the law ofconservation ofenergy is

flawed.

o Pauli took a different approach, and postulated existence of new particle. In decaythis particle would carry away theenergy that is unaccounted for. The particle must

be neutral and it must havevirtually no mass, making it a highly penetrating particle.

Femi named it the neutrino. It waseventually detected, but not until 1953.

Radioactive Decay

decay- This happens in v.big nuclei (>82 protons6 like uranium and radium. Thenuclei ofthese atoms aretoo big for thestrong nuclear force to keep them stable. When alpha

particle isemitted the proton decreases by2 and nucleon number decrease by4:

Repulsive

electromagneti

-c force

Attractive

Nuclear Force


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-d7 8 9

@

Beta-minus is emission of electron from nucleus along with antineutrino.

Happens in isotopes that are neutron rich (i.e. have too many more neutrons than protons

in their nucleus). When nucleus ejects beta particle, one of neutrons in nucleus is changed

into proton. The proton number increases by 1 and nucleon number stays same. A tiny

neutral particle called antineutrino released. This carries energy and momentum away:

+d A B C D See above but opposite. The decay produces a positron (anti-electron) and a

neutrino:

d E F G H electromagnetic radiation

Atomic Discovery

Electrons (discovered by J J Thomson in 1987, Cavendish Lab, Cambridge, though he calledthem negative corpuscles, the name electron was coined by G Johnstone Stoney in 1981

Nuclei were discovered by Rutherford, Geiger and Marsden, 1911. Originally people thoughtthe electrons were scattered randomly in positive cloud (plum pudding model). Their

eI

periment shows most mass in centre of atom and electrons orbit around. All positive

charge in centre. Model accepted quickly as results could be achieved by easily repeating

eI

periment. They fired alpha particles at golden foil and nearly every electron went straight

through but 1:8000 were deflected greatly by the nucleus and some back scattered.

It soon realised that nuclei contained multiples of nuclei of hydrogen atoms (i.e. protons P Rutherford suggested the name proton in 1920)

The simple picture completed by Chadwicks discovery ofneutron (predicted by R) in 1932.It was discovered when detected in a sub atomic particle detection e

Q

periment in a

photographic film. It was detected when ionising radiation consisted of protons emitted

from paraffin waQ

when neutrons hit the nuclei of hydrogen atoms. The neutrons came from

beryllium that had been bombarded with alpha particles.

Particles and Antiparticles

Paul Dirac predicted the eR istence of electrons antiparticle before discovered. The positron found in cloud chamber e S periments with cosmic rays done by Carl Anderson.

Positrons have identical mass (and identical energy in MeV) to electrons but they carry a

positive charge.

It was the first case of theory predicting the e T istence of a particle before its discovery. He later discovered the Muon in the same way. Every particle has a corresponding particle with same mass but opposite charge


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Particle Symbol Charge Antiparticle Symbol Charge

Proton P +1 Antiproton -1

Neutron n 0 Antineutron 0

Electron e -1 Positron +1

Electron-neutrino 0 Electron-antineutrino e 0

When energy isconverted into massyou get e U ual amountsand antimatter. (E=mc2 V Firetwo protonsat each other at high speed and youll end up with a lot ofenergyat the

point of impact. Thisenergy might beconverted into more particles. If an extra proton is

formed then there will always be an antiproton to gowith it. It called pair production.

Particle Tracks

Each particle antiparticle pair isproduced from a singlephoton. Pair production only happens ifone gamma ray photon hasenough energy to produce that

much mass. It also tends to happen near a nucleus, which helpsconserve momentum

You usually get electron-positron pairs produced (rather than any other pair) because theyhave a relatively low massso haveenough energy.

Gamma photons arenot very ionising tend not leave tracks in bubblechamber or cloudchambers.

The opposite of pair-production isannihilation. When a particle meets its antiparticle resultis annihilation.All mass of particle and antiparticle getsconverted back to energy.

Antiparticlescan onlyexist for a fraction of a second before this happens, so you dont get

them in ordinary matter.

Mesons are their own antiparticles. Its worth mentioning that the -meson is just theantiparticle of the+meson and theantiparticle of 0meson is itself.

The particle tracks arecurved b/c theres usuallymagnetic fieldpresent in particle physicsexperiments.

Theycurve in opposite direction b/c of theopposite

charges on electron and positron.

Theelectron and positron annihilation and theirmass areconverted into theenergy of a pair of

gamma ray photons, each ofenergy511 keV. (Both

electron and positron have mass of511 keV/c2).


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Classification of Particles -Baryons

Baryon It was coined to describe the heavy subatomic particles such as protons andneutrons.

Its helpful to think of protons and neutrons as 2 version of same particle the nucleon.Theyjust have different electric charges.

Protons and neutrons are both baryons. There are other baryons that you dont get in normal matter like sigmas () theyre short

lived.

All baryons eW cept proton are unstable and decay to a proton. This means that theydecay to become other particles. The particles a baryon ends up as depends on what it

started as, but it always includes a proton. Proton are only stable baryons they dont decay

Antiparticles of protons and neutrons are antibaryons. Due to annihilation andanitparticles you dont find antibaryons in ordinary matter.

The number of baryons in an interaction is called the Baryon Number. Like nucleon numberbut including baryons like . Proton/Neutron baryon number is B=+1. Antibaryons, B=-1.

Particles that arent baryons areB

=0.W

hen an interaction happens the baryon number oneither side of the equation is the same. You can predict whether an interaction will happen

if numbers dont match wont happen. The total baryon number in any particle interaction

never changes.

Beta decay involves neutron changing into proton. Happens when more neutrons thanprotons in nucleus. Beta decays caused by weak interaction:

e Electrons and antineutrinos arent baryons (theyre lepton), so they have baryon number of

B=0. Neutrons and proton, B=1 interaction happens as sides baryon number =.

Classification of Particles Hadrons

Hadron is a collective term of both mesons and baryons Mesons are a less massive cousin of hadrons with a baryon number of 0 Following discovery of neutron, many particles were discovered, including strange ones. These seem to be created in pairs, encouraging Murray-Gell Mann to allocate strangeness

numbers to some of these particles. In these reactions strangeness was always conserved.

Classification of Particles Mesons

This is a type of hadron. All mesons are unstable and have baryon number of 0 b/c not baryon Pions ( mesons) are the lightest mesons. You get 3 versions with different electric charges

+, 0 and -. Pions were discovered in cosmic rays. You get load of them in high-energy

particle collision CERN particle accelerator

Kaons (-mesons) are heavier and more unstable than pions. You also get K+ and K0. Mesons interact with baryons via the strong force.


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Pions interactionsswap protons with neutrons and neutrons with protons but leave theoverall baryon number unchanged.

Classification ofParticlesPositron

P.A.M Dirac predicted the antiparticle of an electron. It wasconfirmed by Carl Andersonin1932 in a cloud chamber experiment with cosmic rays

It was first case of a predicting a particle before discovery. The Muon was discovered insame way later on.

Like an electron, the positron has a spin of0.5, and an extremely low mass (approx. 1/1836of proton). Its only difference to theelectron is that it has the oppositecharge.

AndersonsPositron Photograph (Experiment):o Acosmic rayenters thecloud chamber and itsenergyconverted into 2 particles.o Positron is moving up the photograph.o Slowed down by passing through lead plate acrosscentre.o Curvaturecaused by magnetic field.o Slower particles bend more b/c it spends longer in the field.o Anderson deduced from curvature and length of path that particle was positive and

had mass not more than twice that of an electron.

Classification ofParticlesLepton (Muon & Taus)

Theyreclass of fundamental particle that dont experiencestrong forceof hadrons. They only really interact with other particlesvia weak interaction (along with a gravitational

force and electromagnetic force as well if theyrecharged) The leptons form an important part of the Standard Model of particle physics. The most famous lepton is theelectron. The other two important Leptons are Muon

chargesX

and Neutrino uncharged. There are a total of12 known leptons.

Electrons arestable. There two more leptonscalled muon () and the tau () that are justlike heavyelectrons.

Muons and taus are unstable, and decayeventually into ordinaryelectrons. Theelectron, muon, tau leptonseach come with theirown neutrino, , and .


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Neutrinos (see below) and have Y ero electric charge. Each lepton is given a lepton number of +1, but the electron muon and tau types of lepton

have been counted separately. You get 3 different lepton numbers, Le, L and L.

Name Symbol Charge Le L LElectron e

--1 +1 0 0

Electron-neutrino 0 +1 0 0

Muon -1 0 +1 0

Muon-neutrino 0 0 +1 0

Tau -1 0 0 +1

Tau-neutrino 0 0 0 +1

Classification of Particles Neutrino

Zero Charge - not affected by electromagnetic forces. Neutrinos have a very small but non- ero mass (Ea . me?) 0


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Quark Symbol Charge Baryon number, B Strangeness, S Spin

Up u - 1/3 0 Down d - -1/3 0

Strange s -

-1/3 -1

Anti-Up - -1/3 0Anti- Down 1/3 0

Anti-Strange s 1/3 1

Rules of Quarks - Baryons

EM interactions are due to a property with two states (+ve and ve). Quark interactions are due to a property with 3 states. This has been called colour change b/c 3 primary colours red, green and blue add to give

white, a colourless combination.

Baryons are composed of3 quarks. Strange baryons contain at least one strange quark

The photon and the + are both uud. The difference between them lies the way quark spinscombine

Each quark is a spin particle. A quark triplet (baryon) can either be spin or spin 3/2depending on whetherjust 2 or all 3 quarks are aligned with spins parallel.

Particles with half integer spin, such as quarks and leptons are known asfemions.

Rules of Quarks - Anti-Baryons

Anti-quarks have an anti-colour. Anti-red = cyan, anti-green = magenta, anti-blue = yellow 3 anti quark combinations are anti-baryons. Anti-baryons are composed of three anti-quarks -

Rules of Quarks Mesons

By combining a quark with an anti-quark of appropriate anti-colour, a two-quark hadronscan be produced. These two-quark combinations are the mesons.

Qu g h k Triplet Strangeness Charge /e Spin

udd 0 0 n0

uud 0 +1 p+

dds -1 -1 7-

uds -1 0 70, 0

0

uus -1 +1 7+


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Mesons arecomposed of a quark and an anti-quarksee below.Quark Pair Strangeness Charge / e Meson (Spin 0)

d 0 -1 T-

u 0 0

T0, L

0, L

0d 0 0

ss 0 0

u 0 +1 T+

s -1 0 /0

s -1 -1 /-

sd +1 0 /0

su +1 +1 /+

Summary of Quarks Hadrons and Definitions

Hadri p A particle made of any number of quarks Baryq r A particle made of3 quarks Mess t A particle made of a quark and an anti-quark

TheStandard Model

Describesinteractions ofelementary particles (except those due to gravity) in terms ofintermediaryvirtual particles (exchange bosons). All ordinary matter as we know it is

constructed from first generation alone

Problems with this model is that:o Doesnt attempt to explain gravitation. It is hard to unitegeneral relativity (theory of

gravitation) and quantum field theory (basis ofstandard model)

o It cannot account for observed number ofelementary particles,matter-antimatterasymmetry, dark matter, dark energy, etc.

Hadrons

Baryons-qqq

Anti-Baryons- qqq

Mesons- qq

yellow blue magenta blue

Allowed quark anti-quark combo Forbidden quark anti-quark combo


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Eu

change Particles

Exchange particle is when two particles interact and a force must be there to show oneparticle that the other ones there

o Repulsion E.g. each time ball is thrown or caught people pushed apart due to ballcarries momentum

o Attraction E.g. each time boomerang thrown or caught people get pushedtogether

The ev change particles are called gauge bow onw The repulsion between two protons is caused by ex change ofvirtual photons, which are the

gauge bosons of the electromagnetic force. Gauge bosons are virtual particles they only

ex

ist for very short time.

Fundamental Forces

Force Particles Affected Gauge Boson Range RelativeStrength

Gravity

Acts between objects

with mass

Allpa

les with

masses

Graviton Infinity Much Weaker

Weak force

Governs particle decay

Qua

ks andLeptons

( All Types)

W+, W-W Short

Range

Electromagneti

m

Acts between electrically

charged particles

Electronically

chargedparticles

only

K

Photon

Infinity

Strong Force

Binds quark together

Hadrons only

(quarks andgluons)

Gluon Short

Range

Much Stronger

The weak force is unusual b/c has 3 e change particles. The first two weak interaction bosons are charged, and are emitted when LHS particle

changes charge.

The larger the mass of the gauge boson , the shorter the range offorceo The W bosons have 100 times mass of proton, which gives weak force very short

range.

o Creating a virtual W particles uses so much energy that it can only e ist for veryshort time and it cant travel far

o Photon has ero mass, which gives a force with infinite range

Feynman Diagrams

RulesI. Time goes vertically up diagram ( many sources have time hori ontal)

II. If particles heading outwarddoesnt mean repel each other


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III. Particlesshown bynormal arrow-heads, anti-particlesbyreversed arrow-headsIV. Gauge bosonsrepresented bywiggly linesV. Other particlesrepresented bystraight lines

TheG

oldL

eaf Electroscope

Red LaserLi t no effect Mai s Li tB l no effect Ultra vi letlam leaf falls immediately

F

-

Decay

Antineutrino produced so

lepton number conserved

F+ Decay

Neutrino produced so

lepton number conserved

Proton CapturingElectron

Electrons and protons attracted by

electromagnetic interaction between

them but if theycollide the weak

interaction can make this happen

Neutrino-Neutrino

CollisionProton-Antineutrino

Collision

Theresvery low

probability of a

neutrino interacting

with matter, but heres

what happens


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The light appears to be liberating free electrons from the inc, discharging the electroscope Observation:

o The photoelectric effect appears to be instantaneouso The light must be energetic enough, which for inc is in ultraviolet region of

spectrum

o The wave theory of light predicts that freeelectrons would steadily absorb energyuntil they escape from the surface

E planation Einstein - See belowThe Photoelectric Effect

Einsteins quantum theory of the photoelectric effect has several important consequences. We think the light as quanta of radiation (photons). Shine light of high enough frequency onto metal, electrons will be emitted.

o Free Electrons on surfaceabsorb energy from light, making them vibrateo If an electron absorbs enough energy, the bonds holding it to the metal break and

electron are released. A single electron captures the energy of a single photon.

o The emission of an electron is instantaneous, so long as the energy of each incomingquantum is big enough

o This is the photoelectric effect and the electrons emitted are photoelectrons There are three main conclusion from the e periment above:

o There is a thre hold frequency(i.e. energy) below which no electrons is released.o Photoelectrons are emitted with a variety of kinetic energies ranging from ero to

some maj

imum value. This value ofmaj

imum kinetic energyincreaseswith the

frequency of radiation, and is unaffected by the intensity of radiation

o Number of photoelectrons emitted per second is proportional to intensity of light As the intensity of the light is increased:

o The electrons are released at a rate proportional to intensity of light (i.e. morephotons per seconds means more electrons released per second).

o The energy of emitted electrons is independent ofintensity of the incident radiation.Wave Theory

Photoelectric effect couldnt be ek plained by wave theory because according to wavetheory:

o For particular frequency of light, energy carried proportional to intensity of beamo Energy carried by light evenlyspread over wavefronto Each free electron on surface of metal would gain bit of energy from each incoming

wave

o Gradually, each electron would gain enough energy to leave metal Wrong b/c

o If light had lower frequency it would take longer for electrons to gain enough energy but would happen

o No threshold frequency


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o The higher the intensity of wave, the more energy it should transfer to each electron the kinetic energy should increase withintensity

o There is no el planationfor the kinetic energy depending on frequency.Photon Model of Light

EM waves only released in discrete packets or quanta. Energy carried by quanta is:

EM waves only em ist in discrete packet called photons He saw these photons of light as having one-on-one, particle-like interactionwith an

electron in a metal surface. It would transfer all its energy to one, specific electron.

According to photon model:o When light hit its surface, metal bombarded by photonso If one of these photons collides with a free electron, the electron will gain energy

equal to

Before an electron can leave the surface of the metal, it must obey the work function () ofthe metal which states that a minimum energy is needed to remove an electron from the

surface of a metal. This value depends on the metal. (See Potential Well)

The theory also en plains the threshold frequency.o If energy gained from photon is greater than work function energy, electron emittedo Ifisnt, electron will vibrate, then release energy as another photon. Metal heat up,

but no electron emitted

o Since, for electrons to be released, , the threshold frequency must be:

The theory also eo plains mao imum kinetic energy:o Energy transferred to an electron is hfo Kinetic energy it will be carrying when leaves metal is :

Thats why range of energies Minimum amount of energy it can lose is the work function energy. Also some of the energy

of photon is used to overcome the work function. The rest remains as KE of the electron. So

ma

imum kinetic energy is:

Kinetic energy of electrons is independent ofintensity b/c only absorb 1photon at a time If we make the voltagejust enough to prevent it from escaping (i.e. its leftover KE is ero)

then the voltage must have increased the effective work function by eV for energy to remain

conserved.

We call this potential the stopping potential Vs . It will be important when come tomeasuring the work function.


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The equation then becomes:

The Potential Well

It takes a certain amount of energy to liberate an electron from the surface of the metal:o They are still attracted to the positive nuclei of the atoms.o The electron is stuck at the bottom of a potential energy well, created by the crystal

lattice of the metal.

The Electron Volt

An electron volt(eV) is the energy that an electron would have if it was accelerated through1 volt.

A volt has units ofJoules per Coulomb: i.e. an object with a charge of 1C accelerated througha voltage of 1V would have 1J of kinetic energy

An electron has a charge of 1.6 X 10-19C. Therefore it has 1.6 X 10-19 J (electron volts)Energy Levels

Electrons in atoms e ist in discrete energy levels. Use electron volt as energy is are tiny An electron can only move directly between such levels, emitting or absorbing individual

photons as it does so.

The energy carried by each proton is equal to difference in energies between the two levels.The equation shows a transition between levels n=2 and n=1

An energy input raises the electrons to higher energy levels. This energy input can be by anymethod.

If the electron is given enough energy to escape the atom then we say that the atom hasbeen ioni

ed

If an electron does not receive the e act energy needed to get to another energy level,nothing happens


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Once electron hasjumped to higher energy level, lets say n=4, it can go back to ground statein any order and not necessarily straight back down. To do this it emits a photon with an

energy equal to the energy gap.

The photon is emitted in random directionEmission Spectra

Electrons are e cited to higher energy levels (by for e ample an electric current) and decayvia a number of routes, emitting photons as they do so

Quantisation

The e planation of the line spectra began with the realisation byBohr that an atomselectron can only e

ist in certain, well-defined orbits each with a particular energy

Bohrs model of electron energy level quantisation predicted that this would happen sincethere was a certain minimum energy that an electron can have (its ground level)

Fluorescent Tubes

They use e

cited electrons to produce light

Fluorescent tubes contain mercury vapour, across which a high voltage is applied When electrons in mercury collide with fast-moving electrons (accelerated by high voltage)

theyre e

ited to a higher energy level.

When these e cited electrons return to their ground states, they emit photons in UV range A phosphorous coating on inside of tube absorbs these photons, ez citing its electrons to

much higher orbits. These electrons then cascade down energy level, emitting many lower

energy photons in form of visible light.

Line Emission Spectra

A line { pectrum is seen as a series of bright lines against black background Each line corresponds to particular wavelength of light emitted by source Since only certain photon energies are allowed, you only see corresponding wavelengths This happens if you split light from fluorescent tube with prism The white light shows a continuous spectrum The gas discharge lamps show line spectra The spectrum of a gas gives a kind of finger print of an atom Astronomers e| amine the light of distant stars and gala | ies to discover their composition

(and a lot else)

Absorption Spectra

Ab} orption } pectra occur when a shining white light through cool gas. Continuous spectracontain all possible wavelengths.

o The spectrum of white light is continuouso If you split the light up with a prism, the colours all emerge into each other there

are no gaps in spectrum

o Hot things emit continuous spectrum


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Line Absorption Spectra

Get this when white light (continuous spectrum) passes through cool gas. At low temperatures, most ofelectrons in gas atoms will be in their ground states. Photons ofcorrect wavelength are absorbed by electrons to e~ cite them to higher energy

levels. The electrons redirect the light in random directions.

This shows us as gaps in the spectrum, b/c wavelengths are missing from continuousspectrum when it comes out the other side of the gas.

You see a continuous spectrum with black lines in it correspond to the absorbedwavelengths.

If you compare the absorption and emission spectra ofa particular gas, the black lines inabsorption spectrummatch up the bright line in the emission spectrum.

Using the suns absorption spectra, scientists can deduce the composition of the sun andindeed other stars.

Photons passing through the sun outer layers are absorbed and remitted in randomdirections, producing a characteristic absorption spectrum.

Wave-Particle Duality

Interference and diffraction show light as waveo Light produces I and D patterns alternating bands ofdark and lighto These can be e plained using Constructive Interference (2 waves overlap in phrase)

and Destructive Interference (2 waves out of phrase)

The photoelectric effect shows light behaving as a particleo Evidence as e periments ofphotoelectric e periments show particle-like photons.o If a photon of light is discrete bundle ofenergy, then it can interact with electron in

one-to-one way

o All energy in photon is given to one electron De Broglie came up with theWave-Particle Duality Theory Ifawave-like lightshowed

particleproperties (photons),particles like electrons shouldbe expectedto showwave-like

properties. Came up with an equation relating wave property (wavelength, P) to moving particle

property (momentum, mv)

Electron diffraction shows theWave Nature ofElectrons.


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o Diffraction patterns are observed when accelerated electrons in a vacuum interactwith spaces in graphite crystal. Confirms wave-like properties

o According to wave theory, spread of lines in diffraction pattern increases if thewavelength of wave is greater.

o In electron diffraction e periments, a smaller accelerating voltage gives widelyspaced rings

o Increase the electron speed and the diffraction pattern circles squash togethertowards the middle. Ifvelocity is higher, the wavelength is shorter and the spread of

lines is smaller.

In general, P for electrons accelerated in vacuum tube is about same si e as electromagneticwaves in X-ray part of spectrum.

Particle dont how wave-like particle all the time.

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