ALEVEL PHYSICS AQA Unit 1 Particles Quantum Electricity NOTES

7/23/2019 ALEVEL PHYSICS AQA Unit 1 Particles Quantum Electricity NOTES

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AS unit 1phya1

particles

quantum phenomena

electricity

GCE PHYSICS

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e 1 o+ '



AS E-amination

Unit 1 . PHYA1 Particles, Quantum Phenomena and ElectricityWritten Examination . 70 marks, 6 or 7 structured questions1 ¼ hours

40% of the total A marks!0% of the total A"#e$el marks a$ailale &une

Unit $ . PHYA$ echanics, aterials and a/esWritten Examination . 70 marks, 6 or 7 structured questions1 ¼ hours40% of the total A marks!0% of the total A"#e$el marks a$ailale &une

Unit In/esti*ati/e and Practical S0ills in AS PhysicsPHA, Externall' (arked )oute * . ++ marks

ractical kills -erification - . teacher $erification/Externall' (arked ractical Assinment E(A . ++ marks/!0% of the total A marks10% of the total A"#e$el marks a$ailale &une onl'

A$ E-amination

Unit ' . PHYA' 2ields and 2urther echanicsWritten Examination . 7+ marks,1 hoursection A is !+ multi2le choice questions, each 3orth one mark.

ection is a 3ritten 2a2er of 45+ structured questions and consists of +0 marks.!0% of the total A"#e$el marks a$ailale &une

Unit ( . 3ne o+ Units PHA(A, PHA(!, PHA(C, PHA(DWritten Examination . 7+ marks.1 hoursection A uclear and 8hermal h'sics . 40 marks9om2ulsor' section 45+ structured questionsection one of the follo3in o2tions.Each 2a2er has 45+ structured questions and :+ marks.;2tions A " Astro2h'sics " (edical h'sics!0% of the total A"#e$el marks ection A 10%, ection 10%/ A$ailale &une onl'

Unit 4 . Internal Assessment In/esti*ati/e and Practical S0ills in A$ PhysicsPHA4, Externall' (arked )oute * . ++ marksractical kills -erification - . teacher $erification/Externall' (arked ractical Assinment E(A . ++ marks/10% of the total A"#e$el marks A$ailale &une onl'

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e $ o+ '



8his module in$ol$es t3o contrastin to2ics in 2h'sics 2article 2h'sics and electricit'. 8hrouh the stud' of theseto2ics, students should ain an a3areness of the on"oin de$elo2ment of ne3 ideas in 2h'sics and of thea22lication of in de2th kno3lede of 3ell"estalished to2ics such as electricit'. article 2h'sics introduces studentsto the fundamental 2ro2erties and nature of matter, radiation and quantum 2henomena. <n contrast, the stud' ofelectricit' in this module uilds on and de$elo2s 2re$ious =9E studies and 2ro$ides o22ortunities for 2ractical 3ork

and looks into im2ortant a22lications.

Syllabus extract:

Constituents of the atom Proton, neutron, electron.Their charge and mass in SI units and relative units.Specific charge of nuclei and of ions.

Atomic mass unit is not required. Proton number Z, nucleon number A, nuclide notation, isotopes

Stable and unstable nucleiThe strong nuclear force; its role in eeping the nucleus stable; short!range attraction to about " fm, ver#!short range repulsion belo$ about %.& fm; 'quations for alpha deca# and ( ! deca# including the neutrino.

Particles, antiparticles and photonsCandidates should no$ that for ever# t#pe of particle, there is a corresponding antiparticle.The# should no$ that the positron, the antiproton, the antineutron and the antineutrino are theantiparticles of the electron, the proton, the neutron and the neutrino respectivel#.Comparison of particle and antiparticle masses, charge and rest energ# in )e*.

Photon model of electromagnetic radiation, the Planc constant, ' + hf +hc-

no$ledge of annihilation and pair production processes and the respective energies involved.The use of ' + mc/ is not required in calculations.

Particle interactionsConcept of e0change particles to e0plain forces bet$een elementar# particlesThe electromagnetic force; virtual photons as the e0change particle.The $ea interaction limited to ( ! , ( 1 deca#, electron capture and electron!proton collisions; 2 1 and 2 ! as the e0change particles.Simple 3e#nman diagrams to represent the above reactions or interactions in terms of particles

going in and out and e0change particles.

Classification of particles 4adrons5 bar#ons 6proton, neutron7 and antibar#ons 6antiproton and antineutron7 and mesons6pion, aon7.

4adrons are sub8ect to the strong nuclear force.Candidates should no$ that the proton is the onl# stable bar#on into $hich other bar#onseventuall# deca#; in particular, the deca# of the neutron should be no$n.

9eptons5 electron, muon, neutrino 6electron and muon t#pes7. 9eptons are sub8ect to the $ea interaction.Candidates $ill be e0pected to no$ bar#on numbers for the hadrons.

9epton numbers for the leptons $ill be given in the data boolet.

:uars and antiquars

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e o+ '



p 6u7, do$n 6d7 and strange 6s7 quars onl#. Properties of quars5 charge, bar#on number and strangeness.Combinations of quars and antiquars required for bar#ons 6proton and neutron onl#7,antibar#ons 6antiproton and antineutron onl#7 and mesons 6pion and aon7 onl#.Change of quar character in ( !and ( 1 deca#.

Application of the conservation la$s for charge, bar#on number, lepton number and strangeness

to particle interactions. The necessar# data $ill be provided in questions for particles outsidethose specified.

Particles and 5adiation

Constituents o+ the Atom

asic tructure of the Atom 8he structure of the atom 3as unkno3n until the earl' !0 th centur'

8he nucleus consists of 2rotons and neutrons at thecenter of the atom.rotons are >/ chared 3hile neutrons are neutral. othha$e similar massesElectrons are "/ chared, 151?00 the mass ofneutrons52rotons, and in motion around the nucleus.

6he 7uclear Atom)utherford thouht α @elium nuclei/ 2articles 3ould e the ideal 2article to 2roe the atom.

@e de$elo2ed his famous old foil ex2eriment to in$estiate the inner structure of theatom. 8his classic diffraction ex2eriment 3as conducted in 111 ' @ans =eier andErnest (arsden at the suestion of Ernest )utherford.

α 2articles 3ere shot at a thin old foil.A Binc sulfide detection screen surroundin the foil 3ould fluorescence 3hene$erradiation struck the screen. 8he old foil had to e as thin as 2ossile to a$oidmulti2le scatterins.=eier and (arsden ex2ected to find that most of the al2ha 2articles tra$el straihtthrouh the foil 3ith little de$iation, 3ith the remainder ein de$iated ' a 2ercent or

t3o. 8his thinkin 3as ased on the 2lum 2uddin model.

What the' found, to reat sur2rise, 3as that most of the α 2articles 2assed rihtthrouh the foil, im2l'in the atom is mostl' em2t' s2ace.A fe3 2articles 3ere 3ildl' deflected, im2l'in a lareconcentration of >/ chare in the center of the atom.)utherfordCs model of the atom included a dense,2ositi$el' chared nucleus containin 2rotons.

Electrons 3ere thouht to orit the nucleus like 2lanets orit the sun.

6he 7eutron

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e ' o+ '



<n 1:!, 9had3ick used 2articles to strike e metal. A $er' 2enetratin t'2e of radiation 3as formed.8his t'2e of radiation had no chare and had a similar mass to a2roton. <t 3as called the neutron.' the earl' 100s, the atomic model consisted of neutrons and2rotons in the nucleus.

7ucleon num"er and 8roton num"er.

7ucleon num"er A/ mass numer/ is the numer of 2rotons 2lus the numer of neutrons in the nucleus i.e. thetotal numer of nucleons.Proton num"er 9/ atomic numer/ is the numer of 2rotons in the nucleus.

<n eneral a nucleus * is re2resented ' A

9

Al2ha 2article 4 !> roton 1 Electron 0 eutron 1 @e @ e n ! 1 "1 0

Isoto8es

83o atoms ma' ha$e the same numer of 2rotons ut different numers of neutrons i.e. the' ha$e the same 2roton

numer ut different nucleon numer. Each atom is said to e an isoto2e of the other. 8he' are chemicall'indistinuishale ecause the' ha$e the same numer of electrons and occu2' the same 2lace in the 2eriodic tale.(ost elements are isoto2ic mixtures.@'droen has three forms

@'droen 1 Deuterium ! 8ritium :@ @ @

1 1 1;rdinar' h'droen contains .% of the @'droen 1 atoms. Water made from deuterium is called hea$' 3ater.

Sta"le and unsta"le nuclei.

9hemical ro2erties of an atom are o$erned ' the numer of 2rotons in the nucleus 2roton numer F/tailit' de2ends on oth the numer of 2rotons and neutrons nucleon numer A/8he term nuclide is used to s2ecif' an atom 3ith a 2articular 2roton"neutron comination.4 :

;i and ;i are isoto2es and nuclides

< 1%

!e and ! are nuclides the' ha$e the same numer of neutrons ut a different numer of 2rotons

' ( Sta"le nuclides

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e ( o+ '



Number of neutrons against numberof protons

0

20

40

60

80

100

120

140

160

0 20 40 60 80 100

Protons

N e u t r o n s

• 8he lihtest nuclides ha$e almost equal numers of 2rotons and neutrons.

• 8he hea$ier nuclides require more neutrons than 2rotons, the hea$iest aout +0% more.

• (ost nuclides ha$e oth an e$en numer of 2rotons and neutrons. 8his im2lies that !2> and !n0 i.e. anal2ha 2article, form a 2articularl' stale comination ox'en, silicon G iron form o$er of the earthCs crust

Unsta"le nuclides

• Disinterations tend to 2roduce ne3 nuclides near the stailit' line and continue until a stale nuclide is

formed.• A nuclide ao$e the line deca's so as to i$e an increase on 2roton numer i.e. eta emission neutron

chanes to a 2roton and electron/• A nuclide elo3 the line disinterates so that its 2roton numer decreases. <n hea$' nuclides this occurs '

al2ha emission.

Sta"ility ;ine

Actual atoms

6heoretical atomsWith 2> H n0

6he "alancin* o+ nuclear e=uations.

Al8ha # ) 5adiation

(ost emitters are hea$' nuclei 2roton numer reater than ?!. <t is elie$ed that an 2article is created some

time efore its emission in the nucleus. 8he deca' of a 2arent nuclide into a dauhter nuclide ' emissionA A " 4 4 !>* I > @e > J

F F " ! !Knstale )ecoilin @ih $elocit'2arent dauhter α 2articleJ is the ener' released in the deca'. 8he nucleus loses 4 nucleons. A and F are alanced across the equation chare and nucleon numer are conser$ed. Each deca' results in a 2recise quantit' of ener' J/, 3hich is s2ecificto each isoto2e. J a22ears as Linetic ener' of the dauhter nucleus and the emitted α 2article. 8he 2articlecarries most of the kinetic ener'.

A t'2ical emitter is thorium"!!? 3hich deca's to radium"!!4




!!? !!4 48h )a > @e > J

0 ?? !

!eta # ) 5adiation

eutron rich nuclei deca' '>

emission. A>

2article is a hih s2eed electron emitted from the nucleus. eati$esin is used to distinuish it from the ? 2article, 3hich is a 2ositron anti2article to the electron/ emitted ' anunstale, 2roton rich nucleus.

A β" 2article is 2roduced 3hen a neutron in the 2arent nucleus deca's. eutrons are normall' stale 3hen containedin the nucleus ut can deca' 3hen the nucleus has too much ener' usuall' due to an excess of neutrons.A eutron deca's into a 2roton ' emittin a > 2article. 8he nucleus chanes to a different element 3ith the samenucleon numer, ut 3ith the 2roton numer increased ' 1

1 1 0 0

n 2 > e > ν > J 0 1 "1 0β" emitted 3ith antineutrino

continuous raneof eneries

A > 2article is created in the nucleus at the instant of deca', 3hen it is eMected at extremel' hih $elocities,a22roachin that of liht. o o$erall chane in nucleon mass ut 2roton numer increases ' 1. 9hare and massnumer are conser$ed.

> emission is accom2anied ' the simultaneous emission of an antineutrino $irtuall' massless, hihl'

2enetratin 2article 3hich is $er' difficult to detect. Each deca' results in the release of a 2recise quantit' of ener'J 3hich is s2ecific to each isoto2e. 8he total ener' released in deca' is shared et3een the dauhter nucleus, the

> 2article and the antineutrino. 8he > 2articles are oser$ed to ha$e a $er' 3ide rane of eneries from almostBero u2 to nearl' the total J $alue of the deca'.

Al is a t'2ical > 2article emitter

! ! 0 0Al i > e > ν > J

1: 14 "1 0

Gamma # γ ) 5adiation

α and β deca' often 2roduce a dauhter nuclide 3hich is in an unstale, excited state. 8his can deca' further 'emittin a 2hoton of electromanetic radiation of $er' hih frequenc'. 8his is a amma ra'. <t causes no chane inthe 2roton and nucleon numers of the 2arent nuclide.

;$erall effect ofγ

ra' emission is to reduce the ener' of the nucleus. 8he nucleus remains unaltered 2h'sicall'

a2art from ha$in less ener'. γ radiation does not consist of 2articles of matter as it is electromanetic radiation of

$er' short 3a$elenth N 1 * 10 "11 m / and $er' hih ener'. γ radiation is indistinuishale from *"ra's or cosmic

ra's of the same 3a$elenth has a se2arate name ecause it is of a different oriin. <t 2roduces $er' littleionisation therefore it is $er' 2enetratin. <n all cases of radioacti$e deca', the ener' released in the deca' comes

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e : o+ '



from the direct con$ersion of a quantit' of matter into ener'. uch a lare amount of ener' is released that there isa measurale chane in the mass of the 2articles in$ol$ed.

Particles, anti8articles and 8hotons

Anti8articles

Oor e$er' t'2e of matter 2article 3eP$e found, there also exists a corres2ondin antimatter2article, or anti2article.Anti2articles look and eha$e Must like their corres2ondin matter 2articles, exce2t the' ha$eo22osite chares. Oor instance, a 8roton is electricall' 2ositi$e 3hereas an anti8roton iselectricall' neati$e. =ra$it' affects matter and antimatter the same 3a' ecause ra$it' is not achared 2ro2ert' and a matter 2article has the same mass as its anti2article. When a matter2article and antimatter 2article meet, the' annihilate into 2ure ener'Q;n the left in the 2re$ious 2icture/ electrons and 8ositrons are 2roduced from 2hotons. 8he' mo$e in o22ositedirections in a manetic field ecause of their o22osite chare.

7eutrinos ha$e no electrical chare the' almost ne$er interact 3ith an' other 2articles. (ost neutrinos 2ass rihtthrouh the earth 3ithout e$er interactin 3ith a sinle atom of it.

eutrinos are 2roduced in a $ariet' of interactions, es2eciall' in 2article deca's. <n fact, it 3as throuh a carefulstud' of radioacti$e deca's that 2h'sicists h'2othesiBed the neutrinoPs existence.

Oor exam2le 1/ <n a radioacti$e nucleus, a neutron at rest Bero momentum/ deca's,releasin a 2roton and an electron.

!/ ecause of the la3 of conser$ation ofmomentum, the resultin 2roducts of the deca' must ha$e a total momentum ofBero, 3hich the oser$ed 2roton and electron clearl' do not.

:/ 8herefore, 3e need to infer the 2resence of another 2article 3ith a22ro2riatemomentum to alance the e$ent.

4/ We h'2othesiBe that an antineutrino

3as releasedR ex2eriments ha$econfirmed that this is indeed 3hatha22ens.

ecause neutrinos 3ere 2roduced in reat aundance in the earl' uni$erseand rarel' interact 3ith matter, there are a lot of them in the Kni$erse. 8heir

tin' mass ut hue numers ma' contriute to total mass of the uni$erse and affect its ex2ansion.

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e @ o+ '



2undamental 2orces #Interactions)

8he uni$erse, exists ecause the fundamental 2articles interact. 8heseinteractions include attracti/e and re8ulsi/e forces, decay, andannihilation.

8here are +our +undamental interactions "eteen 8articles, and allforces in the 3orld can e attriuted to these four interactions.

hatBs the di++erence "eteen a +orce and an interactionA +orce is the e++ect on a 2article due to the 2resence of other 2articles.8he interactions of a 2article include all the forces that affect it, ut alsoinclude deca's and annihilations that the 2article miht o throuh.We call the 2articles 3hich carr' the interactions +orce carrier8articles.

At a +undamental le/el, a +orce isnBt ust somethin* that ha88ens to 8articles. It is a thin* hich is 8assed

"eteen to 8articles.

Iou can think aout forces as ein analoous to the follo3in situation83o 2eo2le are standin on an ice 2ond. ;ne 2erson mo$es their arm and is 2ushed ack3ardsR a moment later theother 2erson ras at an in$isile oMect and is dri$en ack3ards. E$en thouh 'ou cannot see a asketall, 'ou canassume that one 2erson thre3 a asketall to the other 2erson ecause 'ou see its effect on the 2eo2le.

O;)9E 235CE CA55IE5PA56IC;E #!osons)

5E;A6IE S65E7G6H 5A7GE

8);= =#K; 1 10"1+ m

E#E98);(A=E8<9 @;8; 10"! infinite

=)A-<8I =)A-<8; 10": infinite

WEAL W>, W" , F 10"+ 10"1? m

Some +acts a"out +undamental interactionF

• 2riction is caused ' residual electroma*netic

interactions et3een the atoms of the t3o materials.• 7uclear "ondin* is caused ' residual stron*

interactions et3een the $arious 2arts of the nucleus.• 8he 8lanets orit ecause of the *ra/ity that attracts

them to the sunQ E$en thouh ra$it' is a relati$el' 3eakforce, it still has $er' im2ortant effects on the 3orld.

• ea0 and Gra/ity interactions act on neutrinos.

• ea0 W>, W", and F/ interactions ha$e hea/y carriersS

• All 4 interactions act on the 2rotons in our odies.

• =luons are force carriers cannot e isolated.

• =ra$itons =luons ha$e een oser$ed indirectl'./ are force carriers 3hich ha$e not een oser$ed.

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e < o+ '



Grand Uni+ied 6heory #GU6)

8oda', one of the maMor oals of 2article 2h'sics is to unif' the $arious fundamental forces in a =rand Knified 8heor' 3hich could offer a more eleant understandin of the oraniBation of the uni$erse. uch a sim2lification of thetandard (odel miht 3ell hel2 to ans3er our questions and 2oint to3ard future areas of stud'.

h'sicists ho2e that a =rand Knified 8heor' 3ill unif' the stron, 3eak, and electromanetic interactions. 8hereha$e een se$eral 2ro2osed Knified 8heories, ut 3e need data to 2ick 3hich, if an', of these theories descriesnature.

<f a =rand Knification of all the interactions is 2ossile, then all the interactions 3e oser$e are all different as2ectsof the same, unified interaction. @o3e$er, ho3 can this e the case if stron and 3eak and electromanetic

interactions are so different in strenth and effectS tranel' enouh, current data and theor' suests that these$aried forces mere into one force 3hen the 2articles ein affected are at a hih enouh ener'.

9urrent 3ork on =K8 suests the existence of another force"carrier 2article that causes the 2roton to deca'. uchdeca's are extremel' rareR a 2rotonPs lifetime is more than 10:! 'ears.

h'sicists elie$e that as 'ou o ack in time, and the uni$erse 3as hotter, that the four forces se2arated out fromone sinle, sim2le, force. 8here is ex2erimental confirmation that the electromanetic and 3eak nuclear force 3ereonce a sinle force 3e call the electro3eak force.=rand Knified 8heor' =K8/ and 8heor' of E$er'thin 8;E/

8;E

TTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTTT. 9urrent theor'

TTTTTTTTTTTTTTTTTTTTTTTTTTTTT.. 9urrent kno3lede

Classi+ication o+ 8articles

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e 1% o+ '



;rdinar' matter is made u2 of 2rotons, neutrons and electrons. @o3e$er in hih"ener' collisions, man' other2articles can e created. (ost are $er' short"li$ed.(atter 2articles can e di$ided into t3o main rou2s HAD537S and ;EP637S.

;EP637S8hese 2articles exists on their o3n

QUA5S8hese 2articles onl' exist ound toether

9hare H "1 9hare H 0 9hare H > ⅔ 9hare H " ⅓9onstituentsof ordinar'matter

1st Oamil'

E;EC6537#e>))es2onsile forelectricit' and

chemical reactions.

E;EC6537 7EU65I73 #νe)

)arel' interacts 3ith othermatter.

UP #u) D37 #d)rotons are made u2 of t3o u2 quarks and onedo3n quark.

eutrons are made u2 of one u2 quark and t3odo3n quarks.

8hese2articlesexisted in theearl' momentsafter the ian. o3the' are onl'found incosmic ra'sand at 2articleaccelerators

!nd Oamil'

U37 #µ>)A hea$ier relati$e ofthe electron.

U37 7EU65I73 #νµ

)A relati$e of νe

CHA5 #c)A hea$ier relati$e ofthe u2 quark.

S65A7GE #s)A hea$ier relati$e of thedo3n quark

:rd Oamil'

6AU #τ >)A hea$ier relati$e ofthe electron andmuon.

6AU 7EU65I73 #ντ

) 63P #t)8he hea$iest quark

!3663 #")A hea$ier relati$e of thedo3n and stranequarks.


A66E5

;EP637S HAD537S(ade from Juarks/

GAUGE !3S37SOorce carriers/

E;EC6537S #e)

7EU65I73S #ν)

!A5Y37S

: Juarks/

ES37S

! Juarks/

PH3637S #γ)

P53637S #8)

7EU6537S#n)

PI37 #π)

A37 #)U37 #

µ

>)

6AU #τ

>)

G;U37S

EC635!3S37S

#, 9)

G5AI637



;e8tons

#e2tons are fundamental 2articles and cannot e roken do3n into smaller 2articles. #e2ton is a =reek 3ordmeanin Usmall coinV. 8he' do not interact $ia stron forces ut interact 3ith the $ia the other three fundamentalforces. 8here are 6 different Ut'2esV of #e2tons toether 3ith their #e2ton numer

Electron e"/ ositron e>/ Electron neutrino νe/ Electron antineutrino νe/

(uon µ"/ Antimuon µ>/ (uon neutrino νµ/ (uon antineutrino νµ/

8au τ "/ Antitau τ >/ 8au neutrino ντ/ 8au antineutrino ντ/

;e8ton 7um"er

Each #e2ton is desinated a #e2ton umer #/ of >1 and the antile2tons ha$e a le2ton numer of "1.

Conser/ation o+ ;e8ton 7um"er

An im2ortant conser$ation la3 is the conser/ation o+ le8ton num"er. 8his rule is a little more com2licated than theconser$ation of ar'on numer elo3 ecause there is a se2arate requirement for each of the three sets of le2tons,the electron, muon and tau and their associated neutrinos.

8he first sinificant exam2le 3as found in the deca' of the neutron. Whenthe deca' of the neutron into a 2roton and an electron 3as oser$ed, it didnot fit the 2attern of t3o"2article deca'. 8hat is, the electron emitted does

not ha$e a definite ener' as is required ' conser$ation of ener' and momentum for t3o"od' deca'. 8his im2liedthe emission of a third 2article, 3hich 3e no3 identif' as the electron antineutrino.

8he assinment of a le2ton numer of 1 to the electron and >1 to the electron antineutrino kee2s the le2tonnumer equal to Bero on oth sides of the second reaction ao$e, 3hile the first reaction does not conser$e le2tonnumer.

Hadrons

@adrons are not fundamental 2articles and consist of quarks. 8he 3ord @adron comes from the =reek 3ordmeanin Uulk'V. @adrons interact $ia all four fundamental forces. Althouh indi$idual quarks ha$e fractional

electrical chares, the' comine such that hadrons ha$e a net inteer electric chare.

Juarks ha$e een disco$ered ' dee2 inelastic scatterin of electrons. 8he idea is to accelerate electrons to $er'hih eneries, and then allo3 them to interact 3ith a stationar' 2roton, and in$estiate 3hat ha22ens. At hiheneries, the 3a$elenths associated 3ith the electrons are much smaller than the siBe of a 2roton. @ence theelectrons can 2roe distances that are small com2ared 3ith the 2roton " that is, DEE 3ithin the 2roton. @o3e$er,the hih eneries tend to disru2t the 2roton, so that it 2roduces se$eral ne3 2articles hadrons/. 8his means thescatterin is <E#A8<9 ecause the taret has een chaned in the 2rocess.

!aryons are an' hadron 3hich is made of three =uar0s see next section/. Protons are ar'ons ecause the' aremade of to u8 =uar0s and one don =uar0 uud/. o are neutrons udd/. esons contain one =uar0 and one

anti=uar0. ;ne exam2le of a meson is a 8ion π>/, 3hich is made of an u8 =uar0 and a don aniti=uar0. 8he

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e 1$ o+ '



anti2article of a meson Must has its quark and antiquark s3itched, so an anti2ion "/ is made u2 a do3n quark andan u2 antiquark.

ecause a meson consists of a 2article and an anti2article, it is $er' unstale. 8he 0aon L>/, 3hich is made of anu8 =uar0 and a stran*e aniti=uar0 li$es much loner than most mesons, 3hich is 3h' it 3as called strane anda$e this name to the strane quark, one of its com2onents. aons are assined a stran*eness numer of H 1.

8here is 2artial conser$ation of straneness conser$ed durin stron force interactions, ut not 3eak forceinteractions.

Conser/ation o+ !aryon 7um"er

ature has s2ecific rules for 2article interactions and deca's, and these rules ha$e een summariBed in terms ofconser$ation la3s. ;ne of the most im2ortant of these is the conser/ation o+ "aryon num"er. Each of the ar'onsis assined a ar'on numer !1. 8his can e considered to e equi$alent to assinin each =uar0 a "aryonnum"er o+ 1&. 8his im2lies that the mesons, 3ith one quark and one antiquark, ha$e a ar'on numer !%. okno3n deca' 2rocess or interaction in nature chanes the net ar'on numer.

8he neutron and all hea$ier ar'ons deca' directl' to 2rotons or e$entuall' form 2rotons, the 2roton ein the leastmassi$e ar'on. 8his im2lies that the 2roton has no3here to o 3ithout $iolatin the conser$ation of ar'on numer,so if the conser$ation of ar'on numer holds exactl', the 2roton is com2letel' stale aainst deca'.

An extremel' small 2art of the mass of a hadron is due to the quarks in it.

Gau*e !osons

8hese are the exchane 2articles. An Exchane 2article is a $irtual 2article, 3hich ma' exists for onl' a short time,and is the mediator of a force.

When t3o chared 2articles interact, the' do so ' exchanin a /irtual 8hoton. 8he exchane is im2ossile todetect and hence the term $irtual is used to descrie the 2hoton in$ol$ed.

2EY7A7 DIAG5A 8he diaram elo3 re2resents t3o electrons a22roachin then re2ellin each other

e> e>

a 8hotontime

e> e>

s8ace

> decay >

? decay ?

8 #e>) n #e?)

νe νe

n > "oson 8 ? "oson




n 8 ? e> ?νe 8 n ? e? ?

νe

Quar0s and anti=uar0s

8here are six =uar0s, ut 2h'sicists usuall' talk aout them in terms of three 2airs u8&don, charm&stran*e, and

to8&"ottom. Also, for each of these quarks, there is a corres2ondin anti=uar0./ Juarks ha$e the unusualcharacteristic of ha$in a fractional electric chare, unlike the 2roton and electron, 3hich ha$e inteer chares of >1and "1 res2ecti$el'.

8here are three quantum numers associated 3ith quarks• Char*e, ex2ressed as the fraction of the electronic chare. 15: e

H +.:: × 10"!0 9

• !aryon numer

• Stran*eness numer, 3hen there are stran*e quarks.

• Each anti=uar0 has equal and o22osite $alues of chare, ar'on

numer and straneness.

Quark Charge (Q) Baryon number (B)

Do3n d/ "15: 15:K2 u/ >!5: 15:Antido3n NdX/ >15: "15:Antiu2 NuX/ "!5: "15:

• ar'ons are made of three quarksR antiar'ons of three antiquarks.

• (esons are made u2 of one quark and one antiquark.

• =luons ind quarks toetherR the' are suMect to the stron* interaction.

Electroma*netic 5adiation and Quantum Phenomena

Syllabus extract:

The photoelectric effect 2or function φ , photoelectric equation hf + φ 1 '

the stopping potential e0periment is not required.

Collisions of electrons $ith atomsThe electron volt.

Ionisation and e0citation;understanding of ioni<ation and e0citation in the fluorescent tube.

'nerg# levels and photon emission 9ine spectra 6e.g. of atomic h#drogen7 as evidence of transitions bet$een discrete energ# levels inatoms.hf + ' = ! ' /

2ave!particle dualit#

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e 1' o+ '



Candidates should no$ that electron diffraction suggests the $ave nature of particles and the photoelectric effect suggests the particle nature of electromagnetic $aves; details of particularmethods of particle diffraction are not e0pected.de >roglie $avelength5 - + hmv, $here mv is the momentum.

6he 8hotoelectric e++ect

;i*ht as a Particle

@istoricall' there had een a lot of contro$ers' aout the a/e nature of liht, as 2ro2osed ' the Dutch 2h'sicist@ans @u'ens, aainst the cor8uscular model as 2ro2osed ' the headstron <saac e3ton. 8he conce2t of

a/e>8article duality 3as the start of modern 2h'sics in the middle to late ineteenth 9entur'.

We kno3 that liht sho3s 3a$e 2ro2erties such asY )eflectionY )efractionY Diffraction

Y olarisation @o3e$er it can also e sho3n to ha$e 8articulate2ro2erties as 3ell. 9onsider this model

<f 3e s2ra' Must a short "urst, 3e et Must a +e s8otson the screen

8he loner 3e s2ra', the more s2ots a22ear until the 3hole area is co$ered in 2aint

When usin a s2ra' can, 3e donCt notice an' diffraction effects as the 2articles 2ass throuh the stencil. @ardl'sur2risin as the 2aint dro2lets are 8articles, not 3a$es.

o3, if 3e ex2ose a 2iece of 8hoto*ra8hic 8a8er to a short urst of liht 3e 3illsee

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e 1( o+ '



8he intensit' of the imae on a 2hotora2hic 2late increases the loner the 2a2er is ex2osed for. 8hat intensit' isdetermined ' the numer of sil$er rains de2osited. We see that the 8attern of sil$er rains de2osited is random.<t seems that the liht that de2osited the rains 3as actuall' made of 8articles.

8he deate raed on until the disco$er' in the late nineteenth centur' 3ith the disco$er' of the 8hotoelectric e++ect.

6he Photoelectric E++ect.

8he conce2t of a/e>8article duality 3as the start of modern 8hysics in the middle to late ineteenth 9entur'.We can sho3 the 8hotoelectric e++ect 3ith a22aratus like this

1. We chare the electrosco2e 3ith a neati$e chare.!. We ex2ose the reacti$e metal to liht of a lon

3a$elenth, e.. red.:. We oser$e that there is no effect, ho3e$er riht theliht.

4. We then ex2ose the metal to short 3a$elenth liht, e..K-.+. 8his time 3e see that the old leaf dro2s do3n, sho3inthat the electrosco2e is losin chare.6. <t does not matter ho3 riht or dim the K- liht is.7. o effect 3as oser$ed 3hen the electrosco2e 3as2ositi$el' chared.

8he results 3ereetal >rays Ultra>iolet !lue ;i*ht 5ed ;i*ht

(anesium P O O O

Finc P P O O

odium P P P O

9aesium P P P P

8his led to the conclusion that

• Electrons 3ere ein knocked off. )eacti$e metals ha$e outer shell electrons that can e remo$ed easil'.

• )ed liht 3ould not sho3 this effect ho3e$er riht it 3as. o the am2litude of the liht 3a$e 3as notim2ortant. )ed liht onl' 3orked for caesium, 3hich is a $er' reacti$e metal.

• 8here 3as a threshold +re=uency at 3hich this 2henomenon started to occur. #iht 3a$es 3ith afrequenc' hiher than this shorter 3a$elenth/ al3a's sho3ed the effect, 3hate$er the rihtnessR liht

3a$es 3ith a lo3er frequenc' ne$er sho3ed it.• 8he more reacti$e the metal, the lo3er 3as the threshold frequenc'.

• 8his indicated a 8article "eha/iour to liht.

8hese findins led to the notion of liht ein tin' little 2ackets of 3a$e ener' called 8hotons.

Ourther 3ork ' (ax lanck in 100 2roduced the Photon odel o+ Electroma*netic 5adiation. We can sum thisu2 in the follo3in 2oints




• #iht and other electromanetic radiation is emitted in ursts of ener'. We sa' that it is =uantised.

• 8he 2ackets of ener', 8hotons, tra$el in straiht lines.

• When an atom emits a 2hoton its ener' chanes ' an amount e=ual to the 2hoton ener'.

• 8he ener' chanes are discrete amounts or =uanta .

• 8he frequenc' of the liht and the ener' are related ' a sim2le equation

ZE ener' in &R h lanckCs 9onstantR + frequenc' of the radiation in @B[

8he constant h is lanckCs 9onstant 3ith the $alue 6.6 × 10:4 &s Moule seconds, ;8 Moules 2er second/.

We can comine the equation ao$e 3ith the 3a$e equationE H hf and c H fλ

8he oule is the SI unit for ener'. @o3e$er atomic 2h'sicists find the Moule far too i and clums'. Iou 3ould notmeasure the 3idth of 'our desk in kilometres./ o the' use a unit called the electron /olt e-/. 8he electron $olt isthe amount o+ ener*y used 3hen a chare of electronic char*e 2asses throuh a 8otential di++erence o+ 1 /olt.8he chare on an electron is 1.6 \ 10 "1 9, so 1 e 1.4 1% >1< &.

Collisions o+ electrons ith atoms

Alert Einstein de$elo2ed the theor' further to stud' ho3 atoms interacted 3ith 2hotons. @e 2roduced the notion of=uantum 2h'sics, in 3hich electromanetic radiation has a 2articulate nature. 8he essential 2oints of quantumtheor' are

• All electromanetic radiation is emitted in tin' ursts of ener' called 2hotons

• hotons tra$el in one direction onl' and in a straiht line

• When an atom emits a 2hoton its ener' chanes ' the ener' of the 2hoton.

• Ener' contained in a 2hoton is i$en ' E H hf.

Details of this ex2eriment are ;8 needed for the AJA (odule 1 exam. @o3e$er to understand the results, 3eneed to e a3are of 3hat oes on in the ex2eriment

• 8he 2hotocathode is i$en a 2ositi$e $oltae, and the 2hotoanode a neati$e $oltae.

• 8his means that 8hotoelectrons electrons released ' interaction 3ith a 2hoton. ;ne 2hoton releases oneelectron/ are re2elled from the anode.

• <f the electrons ha$e lots of kinetic ener', the' can o$ercome the re2ulsi$e force.

We turn u2 the re$erse $oltae until the electrons 3ith the most kinetic ener' are Must re2elled. 8he $oltae iscalled the sto88in* /olta*e. We can see 3hat is ha22enin in this diaram

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e 1: o+ '

E = hf

E = hc λ



8he totall' unex2ected result is that the ma-imum 0inetic ener*y of the 2hotoelectrons is e-actly the same reardless of the intensit' of the illumination. @o3e$er dim or riht the liht, the maximum kinetic ener' is thesame.

@o3 can 3e ex2lain these oser$ationsS #ook at the diaram

Althouh the diaram is a sim2lification as to 3hat reall' ha22ens, 3e can see that the 2hotoelectrons are released 3ith a ran*e of kinetic eneries. 8he lo3est kinetic ener' is 3here the electron Must manaes to cra3l out. <t 3ille hauled ack 2rett' quickl' ' the electrostatic forces.

We can summarise these findins in three rules, the las o+ 8hotoelectric emission.

1. 8he numer of electrons emitted 2er second de2ends on the intensit' of the radiation.!. 8he 2hotoelectrons ha$e a rane of ener', from Bero to a maximum $alue. 8he maximum $alue is determined

' the frequenc' of the radiation, not the intensit'.:. A minimum $alue for the frequenc' is needed, the threshold +re=uency.8he maximum kinetic ener' has the same /alue in e as the sto88in* /olta*e. 8his stands to reason. Wekno3 that ener' H chare \ $oltae, and that the electron carries a sinle electronic chare 1e H 1.6 \ 10 "1 9/. oif that chare mo$es throuh a 2otential difference, that amount of 3ork is done.

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e 1@ o+ '



8he ra2h sho3s ho3 the ener' ofthe 2hotoelectrons de2ends on thefrequenc' colour/ of the liht

8here has to e a threshold+re=uency elo3 3hich no

2hotoelectrons are emitted, reardlessof rihtness. 8herefore radio 3a$es,ho3e$er stron, 3ill E-E) affect

A 2hoton 3ith a lon 3a$elenthcarries less ener' than one 3ith ashort 3a$elenth. o if the

3a$elenth of a 2hoton is loner thanthe 3a$elenth suested ' thethreshold frequenc', 2hotoelectrons

3ill not e eMected.

EinsteinJs Photoelectric E=uation

When 2hotoelectrons are remo$ed from a metal surface, a certain amount of 3ork has to e done in remo$in them.8herefore the 2hotoelectrons 3ill lose some of their kinetic ener' in order to esca2e the attracti$e field of the2ositi$el' chared nuclei. 8he 3ork required to remo$e the 2hotoelectron is called the or0 +unction. <t is i$en the2h'sics s'mol ] hi " a =reek ca2ital letter ^hC/ and is measured in Moules, or electron $olts.

8he ener' recei$ed from a 2hoton is s2lit into• 8he 3ork necessar' to se2arate the electron from the metal the 3ork function/

• 8he kinetic ener'.

Ener' of hoton H 3ork done to remo$e electron > kinetic ener' of the electron

We must note the follo3inEk is the ma-imum 0inetic ener*y the chare \ sto22in $oltae/, i.e. the kinetic ener' of the fastest electrons.We are not interested in slo3er electrons.

8he maximum kinetic ener' is de2endent onl' on the frequenc', ;8 the intensit'. A more intense eam 2roducesmore 2hotons 2er second, ut each 2hoton has the same ener'.

We can 3ork out the 3ork function of an' metal ' 2lottin the maximum ener' aainst the frequenc'

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e 1< o+ '

E K ? E0

E K ? Lm/$



We find that the *radient of this ra2h is constant, reardless of the metal. 8he equation of the ra2h is

E0 h+ > K o the radient is lanckCs constant, h.

Also

Ener*y ;e/els in Atoms

Atoms can interact 3ith 2hotons of lo3er ener' than is required to remo$e electrons from them. 8he 2hotons 3e

looked at in the 2hotoelectric effect could remo$e the electrons from $er' reacti$e metals like caesium. hotons caninteract 3ith other atoms to i$e them extra ener', 3hich makes them e-cited.

When 3e heat a as or 2ass an electric current throuh it 3e can make it lo3. We ha$e ionised the as. <f 3elook at the lo3in as throuh a s8ectrometer, 3e see the s8ectrum of the as 3hich is distincti$e for that as.

8here are three 2rinci2al t'2es of s2ectra 3hich a22ear 3hen the liht from an oMectis roken u2 into its com2onent 3a$elenthsor dis2ersed

• a continuous s2ectrum orcontinuumR the emission of athermal s2ectrum is one t'2e ofcontinuum.

• an asor2tion s2ectrum orsometimes an asor2tion"lines2ectrum.

• an emission s2ectrum or emission"line s2ectrum.

An a"sor8tion s8ectrum is 2roduced 3hen a continuum 2asses throuh cooler as. hotons of the a22ro2riateeneries are asored ' the atoms in the as. Althouh the 2hotons ma' e re"emitted, the' are effecti$el'

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e $% o+ '

K h+% hc λ

h+ K ? E0

http://csep10.phys.utk.edu/astr162/lect/light/absorption.html

http://csep10.phys.utk.edu/astr162/lect/light/absorption.html



remo$ed from the eam of liht, resultin in a dark or asor2tion feature. 8he atmos2heres of stars act as a coolerlanket around the hotter interior of a star so that t'2ical stellar s2ectra are asor2tion s2ectra.Knlike the s2ectrum of the un, in 3hich 3e see all the colours of the raino3, 3e onl' see certain colours, 3hileothers are asent. We call this kind of s2ectrum a line emission s8ectrum. 8he colours are discrete 3a$elenths

When a as is ionised, one or more outer electrons are ri22ed off. 8he molecule has ecome 2ositi$e. <t 3illrecomine 3ith an electron and lose ener', i$in that ener' in the form of a 2hoton. ;ther atoms ma' not ha$eeen ionised, ut are still in a $er' excited state. 8he atoms ha$e interacted 3ith the 2hoton and the electrons ha$emo$ed to a hi*her ener*y le/el.

Aout a microsecond later, the electrons lose their ener' as a 8hoton and return to the stale state, called the*round state. 8he im2ortant thin to rememer is that electrons can onl' exist at 8ermitted ener*y le/els. <tCslike a 2erson standin on a ladderR he can exist at one run u2, t3o runs, etc., ut ;8 at a heiht of 1.+ runs.

As 3e consider ener' le$els in atoms, 3e 3ill look at hydro*en 3hich fits this model 3ell. @'droen has oneelectron./ (ore com2lex atoms 3ith se$eral electrons do not.

<f 3e look at a s2ectrum of h'droen, 3e find lines at se$eral discrete 3a$elenths.

Each line re2resents the ener' of a 2hoton as the electron makes a transition from a hiher ener' le$el to alo3er. 8his 3e can sho3 in a diaram elo38he electron does a Mo of 3ork in releasin a 2hotonR it has lost 2otential ener'. 8herefore 3e start at the hi*hest le$el 3hich 3e i$e a $alue of Mero. 8herefore the electron falls from the Bero 2oint to the :.41 e- le$el. 8he moreneati$e the le$el, the lo3er the ener' le$el.

8he hihest ener' le$el is 3here ionisation occurs. 8he lo3est le$el is the round state.

Electrons can make transitions from an' ener' le$el to an' other

8hese transitions i$e us 2hotons in the /isi"le s8ectrum. <n fact,the round state is at 1:.6 e-. 8his is the ionisation ener*y of

h'droen, the ener' required to stri2 an electron from the atom.

We need to e a3are of the follo3in 2oints

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e $1 o+ '



Electron ener*y le/els in Hydro*en

• 8he lo3est le$el "1:.6 e-/ is the round state. 8his is the normal confiuration of the atom. Ener' muste 2ut in to raise the electron to other le$els.

• 8he hihest le$el is the ionisation ener'.

• Ener' le$els are not e$enl' s2aced.

We can quantif' this in an equation. <f an electron is at an excited le$el E1/ and makes a transition to a lo3er le$elE!/, then the ener' of the 2hoton i$en out can e 3orked out 3ith the equation

E E1 N E$ ince E h+, 3e can re3rite this as h+ E1 N E$

2luorescent lam8s

8he central element in a fluorescent lam2 is a sealed *lasstu"e. 8he tue contains a small it of mercury and an inertas, t'2icall' ar*on, ke2t under $er' lo3 2ressure. 8hetue also contains a 8hos8hor 8oder, coated alon theinside of the lass. 8he tue has t3o electrodes, one ateach end, 3hich are 3ired to an electrical circuit. 8he

electrical circuit, 3hich 3ePll examine later, is hooked u2 toan alternatin current A9/ su22l'

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e $$ o+ '



When 'ou turn the lam2 on, the current flo3s throuh the electrical circuit to the electrodes. 8here is a considerale$oltae across the electrodes, so electrons 3ill mirate throuh the as from one end of the tue to the other. 8hisener' chanes some of the mercury in the tue from a liquid to a as. As electrons and chared atoms mo$ethrouh the tue, some of them 3ill collide 3ith the aseous mercur' atoms. 8hese collisions excite the atoms,um2in electrons u2 to hiher ener' le$els. When the electrons return to their oriinal ener' le$el, the' release

liht 2hotons.8he electrons in mercur' atoms are arraned in such a 3a' that the' mostl' release liht 2hotons in the ultra/iolet 3a$elenth rane. ;ur e'es donPt reister ultra$iolet 2hotons, so this sort of liht needs to e con$erted into $isileliht to illuminate the lam2.Phos8hors are sustances that i$e off liht 3hen the' are ex2osed to liht. When a 2hoton hits a 2hos2hor atom,one of the 2hos2horPs electrons Mum2s to a hiher ener' le$el and the atom heats u2. When the electron falls ackto its normal le$el, it releases ener' in the form of another 2hoton. 8his 2hoton has less ener' than the oriinal2hoton, ecause some ener' 3as lost as heat. <n a fluorescent lam2, the emitted liht is in the $isile s2ectrum ""the 2hos2hor i$es off hite li*ht 3e can see. (anufacturers can $ar' the colour of the liht ' usin differentcominations of 2hos2hors.

a/e !eha/iour o+ Particles

8he elian 2h'sicist de !ro*lie reasoned that if 3a$es ha$e a 2articulate 2ro2erties, it 3as reasonale to su22osethat 2articles had 3a$e 2ro2erties. @e de$ised the relationshi2, 3hich states that 2articles ha$e 3a$e 2ro2erties. <tis the loical extension of the 2articulate nature of electromanetic 3a$e 2henomena.

@e comined the follo3in equationsEner' of 2hotons E h+EinsteinCs mass equi$alence E mc$ 8herefore h+ mc$

o3 + c&λ o mc h/λ 8he term mc is mass * $elocit', 3hich is momentum. We i$e momentum the s'mol 8We can re3rite the equation as

λ H h52 or λ H h5m$8herefore e$er' 2article 3ith a momentum has an associated de !ro*lie a/elen*th, e$en somethin as asurd asa car tra$ellin at !0 m5s.

Electrons can e sho3n to ha$e 3a$e 2ro2erties ' the sim2le use of an electron diffraction tue. A slice of caronis 2laced in a eam of electrons so that the electrons diffract.




We need to note a cou2le of 2oints

λ

is the de !ro*lie a/elen*th

8he 3a$e 2ro2erties of electrons ha$e led to the de$elo2ment of the electron microsco8e, 3hich allo3smanifications much ier than 3as e$er 2ossile 3ith the liht microsco2e. A ood liht microsco2e can manif'u2 to 1000 times. 8he electron microsco2e can manif' u2 to aout 1 million times, and can re$eal the existence ofindi$idual atoms. 8he electron eams are focused ' manets Must like the lenses on a microsco2e.

Current Electricity

Syllabus extract:

Charge, current and potential difference 'lectric current as the rate of flo$ of charge; potential difference as $or done per unit charge. I +?:?t, and * + 2:

@esistance is defined b# @ + *I

Current voltage characteristics 3or an ohmic conductor, a semiconductor diode and a filament lamp;Candidates should have e0perience of the use of a current sensor and a voltage sensor $ith adata logger to capture data from $hich to determine * I curves.

Bhms la$ as a special case $here I ∝ *.

Circuits 6part7 'nerg# ' + I * t, P + I*, P + I / @; application, e.g. nderstanding of high current requirement for a starter motor in a motor car.

@esistivit# D + @A9 Eescription of the qualitative effect of temperature on the resistance of metal conductors andthermistors. Applications 6e.g. temperature sensors7Superconductivit# as a propert# of certain materials $hich have <ero resistivit# at and belo$ acritical temperature $hich depends on the material. Applications 6e.g. ver# strongelectromagnets, po$er cables7.

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e $' o+ '



Circuits 6part7 @esistors in series5 @T + @= 1 @/ 1 @" 1 F @esistors in parallel5 =@T + =@= 1 =@/ 1 =@" 1 FConservation of charge and energ# in simple d.c. circuits.The relationships bet$een currents, voltages and resistances in series and parallel circuits,

including cells in series and identical cells in parallel.:uestions $ill not be set $hich require the use of simultaneous equations to calculate currents or potential differences.

Potential divider The potential divider used to suppl# variable pd e.g. application as an audio volume control.

'0amples should include the use of variable resistors, thermistors and [email protected] use of the potentiometer as a measuring instrument is not required.

'lectromotive force and internal resistance∈ + ':

∈ + I6@ 1 r7 Applications; e.g. lo$ internal resistance for a car batter#.

Alternating currentsSinusoidal voltages and currents onl#; root mean square, pea and pea!to!pea values for

sinusoidal $aveforms onl#. I rms + I o G/; * rms + * o G/ Application to calculation of mains electricit# pea and pea!to!pea voltage values.

Bscilloscopese of an oscilloscope as a d.c. and a.c. voltmeter, to measure time intervals and frequencies andto displa# a.c. $aveforms. Ho details of the structure of the instrument is required but familiarit#$ith the operation of the controls is e0pected.

Current and Char*e8he ase electrical quantit' is current, the flo3 of chare. All other electrical quantities are deri$ed from it. 9urrentis measured in am8Ores, or am8s A/. 9hare is measured in coulom"s 9/, 3hich is defined as

1 coulom" is the =uantity o+ char*e carried 8ast a *i/en 8oint i+ a steady current o+ 1 am8 +los +or 1second.

1 electron carries a chare of 1.4×

1%>1< C. 1 coulom is equi$alent to 6.!×

101? electrons.9hare and current are linked ' a sim2le formula

9hare 9/ H current A/ * time s/

8here are some im2ortant multi8liers for current• 1 microam2 1_A/ H 1 * 10 "6 A• 1 milliam2 mA/ H 1 * 10 ": A

Cells and !atteries

9hemical reactions inside a cell hel2 to create a small P36E76IA; DI22E5E7CE et3een the terminals andthis makes the electrons flo3 alon an' conductin 2ath that connects them.

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e $( o+ '

Q = It I = ΔQ Δt



A current flo3 of chare/ 3ill flo3 throuh an electrical com2onent or de$ice/ onl' if there is a $oltae or 2otentialdifference 2.d./ across its ends. 8he ier the 2otential difference across a com2onent, the ier the current thatflo3s throuh it.

8he conductin 2ath throuh the uls, 3ire and atter' is called a circuit.

Ener*y +rom a Cell

8he cell is a source of Chemical 8otential ener*y. <t does 3ork on electrons and the electrons ain Electrical8otential ener*y 3e call it Must 8otential ener*y/.

P.D. #Potential di++erence or olta*e) across "attery terminals. 8he 8.d. or /olta*e across the terminals of thecell indicates the 8otential ener*y i$en to each coulom" a22roximatel' 101? electrons/ of chare.

<f 1 oule of ener' is i$en to 1 Coulom" of electric chare ' the atter' then 3e sa' that the 2.d. across the cellis 1 olt.

When the chares mo$e throuh the 3ire the' do not lose an' of the 2otential ener' the' are carr'in. When the'2ass throuh somethin that resists their flo3, the' 3ill ha$e to do 3ork.

Potential Di++erence

otential Difference is defined as ener*y 2er unit char*e.8he unit of 2otential difference is the $olt -/. Ksin the definition, 3e can define the $olt as &oules 2er 9oulom.

1 - H 1 &9

"1

otential difference is often referred to as /olta*e.

5esistance

)esistance is defined ' the follo3in equation

5esistance 8.d. across conductor Current throu*h conductor

A conductor has a resistance o+ 1 if a current o+ 1A flo3s throuh it 3hen a 8.d. o+ 1 is a22lied across its ends.

otential difference, current and resistance are related as sho3n

8he current throuh a resistor at constant tem2erature/ is 2ro2ortional to the $oltae across the resistor.8he resistance of a conductor increases

• as the tem2erature of the conductor increases.

• as the thickness of the conductor decreases

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e $4 o+ '

V = w Q

8otential di++erence current - resistance #/olt, ) #am8ere, A) #ohm, )

I 5



• as the lenth of the conductor increases

Ener*y and Poer in Circuits

When ener' chanes from one form to another in a resistor, the 8oer indicates the rate ho3 quickl'/ at 3hichthis takes 2lace.

u22ose a current I flo3s for t seconds in a com2onent. 8he chare that flo3ed led to E Moules ein dissi2ated inthe com2onent.We kno3 that Q = It , E = QV

o if 3e sustitute Q out of the second equation, 3e et E = ItVo3

o3er H ener'

timeo 3e can 3rite P = ItV t8he 2o3er out2ut of a cell de2ends on the 2.d. across its terminals and the current it su22lies.

o3er is measured in atts W/. 1 3att H 1 Moule 2er second6he Heatin* E++ect o+ a Current

We kno3 that V = IR and P = IV o 3e can 3rite P = I x IR

We kno3 that: I = V/R and P = IV o 3e can 3rite P = V x V/R

3hmJs ;a

)esistance is the ratio of the $oltae to the current, descried in the sim2le equation R = V/I. <n a metallicconductor, 3e find that if 3e alter the $oltae or the current, the other $ariale chanes in such a 3a' that the ratio

remains constant.

8his is 3hmJs ;a, 3hich states 6he current in a metallic conductor is directly 8ro8ortional to the 8otentialdi++erence "eteen its ends 8ro/ided that the tem8erature and other 8hysical conditions are the same. A conductor that oe's ;hmCs #a3 is called an ohmic conductor.

olta*e Current Characteristics

We can easil' measure $oltae and current, usin the data to 2lot $oltae currentra2hs. We use the follo3in circuit

Orom this circuit 3e take readins of $oltae and current 2lottin them as a ra2hcalled a VI characteristic.

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e $: o+ '

Poer ener*y chan*e time ta0en

Poer 8otential di++erence - current#atts, ) #olts, ) #Am8s, A)

P I

P I2R

P 2/R



We normall' 2ut the $oltae on the '"axis and current on the x"axis. 8his allo3s us to determine the resistance fromthe radient. 8his is a $oltae current ra2h for an ohmic conductor

8he straiht line sho3s a constant ratio et3een $oltae andcurrent, for oth 2ositi$e and neati$e $alues. o 3hen the$oltae is neati$e, the current is neati$e, i.e. flo3in in the

o22osite direction. ;hmCs #a3 is oe'ed. We call this an3hmicconductor.

Oor a +ilament lam8 3e see 8he resistance rises as the filament etshotter, 3hich is sho3n ' the radient ettin stee2er.

A thermistor a heat sensiti$e resistor/ eha$es in the

o22osite 3a'. <ts resistance oes do3n as it ets hotter.8his is ecause the material releases more electrons to eale to conduct.

Althouh it looks similar to the ra2h ao$e, notice ho3 theradient is decreasin, indicatin a lo3er resistance. As thecurrent oes u2, the thermistor ets hotter. As it ets hotter,it allo3s more current to flo3R therefore it ets hotter and so

on.

8his is called thermal runa3a', and is a feature of man' semi" conductor com2onents. At the extreme the

com2onent 3ill lo3 red"hot, then s2lit a2art.

Diodes are semi"conductor de$ices thatallo3 electric current to flo3 one 3a' onl'.8he diode characteristic ra2h looks likethis

8he diode starts to conduct at a $oltae ofaout >0.6 -. We call this +orard "ias.8hen the current rises ra2idl' for a smallrise in $oltae. <f the current is re$ersedre/erse "ias/ almost no current flo3s untilthe "rea0don /olta*e is reached. 8hisusuall' results in destruction of the diode.

5esisti/ity

8he resistance of a 3ire de2ends on three factors• the lenthR doule the lenth, the resistance doules.

• the areaR doule the area, the resistance hal$es.

• the material that the 3ire is made of.

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e $@ o+ '



5esisti/ity is a 2ro2ert' of the material. <t is defined as the resistance of a 3ire of the material of unit area and unitlenth.8he formula for resisti$it' is

Remember: 1 mm! H 1 x 10"6 m!

Series and Parallel Circuits

Series Circuits<n a series circuit, the electrons in thecurrent ha$e to 2ass throuh all thecom2onents, 3hich are arraned in aline. 9onsider a t'2ical series circuit in

3hich there are three resistors of $alue)1, )!, and ):. 8he $alues ma' e thesame, or different.

• 8he current throuhout the circuit is the same

• 8he $oltaes add u2 to the atter' $oltae.

8herefore VT = V1 + V2 + V3 Orom ;hmCs #a3 3e kno3 VT = IR TR

8hus IR T = IR 1 + IR 2 + IR 3

8herefore

' addin* resistors in series, the total resistance of the circuit increases. <f t3o or more resistors are connected inseries, the' i$e a hi*her resistance than an' one of the resistors ' itself.

Parallel 5esistorsarallel circuits ha$e theircom2onents in 2arallelranches so that an indi$idualelectron can o throuh one ofthe ranches, ut not theothers. 8he current s2lits intothe numer of ranches there

are. #ook at this circuit

<n this case, the current 3ills2lit into three.

• 8he $oltae across each ranch is the same

• 8he currents in each ranch add u2 to the total current.

Orom this 3e can 3rite: IT = I1 + I2 + I3 Orom ;hmCs #a3, IT = V/R T , 3e can 3rite

V = V + V + V

R T R 1 R 2 R 3

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e $< o+ '

5esisti/ity # m ) 5esistance # ) - Area # m$ ) ;en*th # m )

56 51 ? 5$ ? 5

1 1 ? 1 ? 1

56 51 5$ 5



' addin* resistors in 2arallel, the total resistance of the circuit decreases. <f t3o or more resistors are connectedin 8arallel, the' i$e a loer resistance than an' one of the resistors ' itself.

irchho++Bs ;as

8hese t3o sim2le la3s 3ere dra3n u2 in the ineteenth 9entur' ' =usta$ )oert Lirchhoff. 8he' ex2lain alloser$ations 3e see in electric circuits. We can ex2lain e$er'thin 3e ha$e looked at in series and 2arallel circuitsin terms of the t3o la3s. 8he' can also e used to ex2lain more difficult circuits 3hich cannot e ex2lained in termsof sim2le series and 2arallel circuits.

irchho++ I F 6he al*e"raic sum o+ currents at a unction is Mero.6his states that the total current +loin* into a 8oint is e=ual to thecurrent +loin* out o+ that 8oint.

<n other 3ords, the chare does not leak out or accumulate at that 2oint.9hare that flo3s a3a' must e re2laced. <t is conser/ed.

Orom this diaram 3e can easil' see that I3 = I1 + I2.(athematicall' 3e can 3rite this as: I1 + I2 + (-I3) = 0

;r Σ I = 0

irchho++ IIF Around a closed circuit loo8, the al*e"raic sum o+ the e.m.+.s is e=ual to the al*e"raic sum o+the 8.d.s. 6he 8otential di++erences around a circuit add u8 to Mero.

ro$ided the chare returns to the same 2lace as it started, the ains and losses are equal, no matter hat routeis ta0en "y the char*e. 8he atter' in this circuit has an em+ electromoti$e force or o2en terminal $oltae/ of ε.

8he curl' ε is the atter' $oltae.

E2 and Internal 5esistance

!atteries or more strictl' s2eakin cells/ con$ert chemical ener*y into electrical ener*y. =enerators turn 0ineticener*y into electrical ener'. <n doin so, the' kee2 the neati$e terminal 3ith an e-cess of electrons and the2ositi$e terminal 3ith a de+iciency of electrons. A atter' does a Mo of 3ork in 2um2in the electrons around thecircuit. ositi$e chares do not mo$e.

8he earl' da' 2h'sicists ot it 3ron 3hen the' said that electric current flo3s from 2ositi$e to neati$e. 8he' didnPtkno3 aout electrons. When the mistake 3as disco$ered, the' decided to stick to the 2ositi$e to neati$e, so allcon/entional current flo3s from 2ositi$e to neati$e.

A atter' is said to 2roduce Em+ electromoti$e force/ 3hich is defined as the ener*y con/erted into electricalener*y hen unit char*e 8asses throu*h the source. `/ <t re2resents the total ener' that can e su22lied to acircuit. E(O is a $oltae.

A ood 3orkin definition of emf is the o2en circuit terminal $oltae of the atter', i.e. 3hen there is no currentflo3in. Althouh the old text ooks had a com2lex method for measurin emf usin a metre ride, no3ada's adi*ital multimeter 3ill i$e 'ou a ood readin as it takes a $er' small current indeed.

8he ener' su22lied to a circuit ' a atter' is i$en '

Where

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e % o+ '

ε = Q



is the ener' in &Q is the chare in 9`, curl' E is the 2h'sics s'mol for emf.

o circuit at all is 100 % efficient. ome ener' is dissi2ated in the 3ires, or e$en in the atter' itself.

Internal 5esistanceAll atteries and enerators dissi2ate heat internall' 3hen i$in out a current, due to internal resistance. A8er+ect "attery has no internal resistance, ut unfortunatel' there is no such thin as a 2erfect atter'. ickel"9admium and #ead"Acid atteries ha$e $er' lo3 internal resistance, and 3e can reard these as almost 2erfect.8hese atteries can 2ro$ide $er' hih currents.

u22ose 3e connect a cell to a hih resistance $oltmeter. A 8er+ect /oltmeter has in+inite resistance. A di*ital multimeter has a /ery hi*h resistance, so needs a tin' currentR it is almost 2erfect. An ordinar' mo/in* coil/oltmeter has a relati/ely lo resistance, so it takes a small ut a22reciale current./

<n this circuit the $oltmeter reads $er' nearl'/ the emf.

u22ose 3e no3 add a load. We 3ill assume the 3ires ha$e ne*li*i"leresistance.

8his time 3e find that theterminal $oltae oes do3n to-. ince - is less than `, thistells us that not all of the $oltae is ein transferred to the outsidecircuitR some is lost due to the internal resistance 3hich heats theatter' u2.

Emf H Kseful $olts > #ost $olts

o 3e can re2resent the circuit as

o our cell is no3 a 8er+ect "attery in series ith an internalresistor, r. Iou cannot o2en u2 the atter' to find the internalresistorR it is 2art and 2arcel of the atter'.

We can no3 treat this as a sim2le series circuit and 3e kno3 that thecurrent, <, 3ill e the same throuhout the circuit. We also kno3 the$oltaes in a series circuit add u2 to the atter' $oltae.

Emf H $oltae across ) > $oltae across the internal resistance

We also kno3 from ;hmCs #a3 that - H <) and $ H <r, so 3e can 3rite

ε H IR + Ir or ε H I (R + r)

All 'ou ha$e to do is turn the cell 3ith the internal resistance into a 8er+ect "attery in series 3ith its internalresistor, and treat it as a sim8le series circuit.

Alternatin* Currents


ε e-t ? lost



Direct current from a atter' mo$es in one direction onl', from 2ositi$e to neati$e. <n alternatin* current thedirection is chanin all the time. 8he chare carriers are mo$in for3ards and ack3ards man' times a second. <nEuro2e it is +0 @B c'cles 2er second/R in the KA 60 @B.

A9 and D9 are equall' ood at heatin, lihtin, or runnin motors. A9 is much more easil' distriuted than D9.8his is ecause transformers use A9 onl'. o electricit' is distriuted at $er' hih $oltaes !7+ k-/ at relati$el' lo3currents. As a result onl' a small 2ro2ortion of the transmitted ener' is lost as heat in the 3ires.

8he ra2h elo3 sho3s the difference et3een A9 and D9.• ;ne com2lete alternation is called a cycle • 8he +re=uency is the numer of c'cles 2er second. Knits are HertM @B/.

• 8he 8eriod is the time taken for one c'cle. <t is measured in seconds. f H 158.

• 8he current follo3s exactl' the same 3a$e form as $oltae.

• 8he ra2h is called a sinusoidal a/e+orm or a sine a/e.

8hese features are sho3n on the ra2h

5oot ean S=uare alue

8he $alues of $oltae and current are constantl' chanin in A9, unlike in D9 in 3hich the' are stead'. We canmeasure A9 $oltaes in t3o 3a's

•

(easure the 8ea0 to 8ea0 $oltae, easil' done on a cathode ra' oscillosco2e 9);/.• (easure the root mean s=uare rms/ $alue, or the e++ecti/e $alue.

We use the rms /alue ecause its use allo3s us to do electrical calculations as i+ they ere direct currents.


Ir!s = I0

"2Vr!s = V0

"2



Ho Does the Poer ary

otice that 2o3er $aries from amaximum of >! to a minimumof 0. 8herefore the a$erae2o3er is . We ne$er et a

neati$e 2o3er, since that 3ouldim2l' that the com2onent 3ascreatin ener'.

6he Cathode 5ay3scillosco8e

8he 9); is connected in exactl'the same 3a' as a /oltmeter,i.e. in 8arallel 3ith a com2onent.8he in2ut resistance is $er' hihand the electron eam acts as a2ointer of neliile inertia. <t is also roust and noteasil' damaed ' o$erloadin. 8he 9); can e used asa D9 $oltmeter. We et a horiBontal line or a dot,de2endin 3hether the time "ase is on. <f it is used as anA9 $oltmeter, it 3ill sho3 the sinusoidal 3a$eform

8he most im2ortant controls that 3e use are

• 8he /ertical sensiti/ity or '"ain settin, calirated in -5cm.

• 8he time "ase, in s5cm.

8he 9); is a 2erfect $oltmeter as its in2ut resistance is $er' hih.

)ememer

• We measure the /olta*e on the /ertical axis. We can adMust the sensiti$it' ' turnin the kno marked y>

*ain or /olta*e *ain.• 8he horiBontal direction is determined ' the time "ase settin. We can chane this ' usin the time

"ase kno.

As 3ell as anal'sin the 3a$eform, there are t3o measurements 3e can make 3ith the 9);

• We can determine the 2eak $oltae of the A9 3a$eform sho3n elo3.• We can also read the 2eriod, 3hich in turn allo3s us to 3ork out its frequenc'.

Unit 1 PHYA1 Particles, Quantum Phenomena and Electricity Dr. ! Cuth"ert #$%&%'&$%1() Pa*e o+ '



otice that

• 8he 8ea0 to 8ea0 /olta*e is 1!.? -. ;ften enineers read the 2eak to 2eak $oltae off the 9); as the

determination of the 0 le$el is not al3a's eas'. 8he 8ea0 /olta*e is half of the 2eak to 2eak $oltae.• 8he root mean square $oltae, 3hich 3e use in electrical calculations, is the 2eak $oltae di$ided ' !

• 8herefore the -rms H 6.4 * ! H '.(

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ALEVEL PHYSICS AQA Unit 1 Particles Quantum Electricity NOTES