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Part 1 - Particles

1 GWC Revised Higher Physics 12/13 HIGHER PHYSICS

1) THE

Can you talk about:

a) Orders of Magnitude

• The range of orders of magnitude of length from the very small (sub- nuclear) to the very large (distance to furthest known celestial objects).

b) The Standard Model of Fundamental Particles and Interactions

• The evidence for the sub-nuclear particles and the existence of .

• Fermions, the particles, consist of: • (6 types) • (, and Tau, together with their ). • Hadrons are composite particles made of Quarks. • Baryons are made of three Quarks • are made of two Quarks. • The mediating particles are bosons: (, and ). • Description of beta decay as the first evidence for the .

2 Orders of Magnitude Powers of Ten video In Physics it is necessary to measure extremely small and extremely large objects, from subatomic particles to the size of the .

The average distance from the Earth to the Sun is 150 000 000 km. There are two problems with quoting a measurement in this way: the inconvenience of writing so many zeros, the uncertainty in the value (How many significant figures are important?) These are over come if scientific notation is used. 150 000 000 km = 1.5 x 108 km

http://www.bcscience.com/bc9/images/0_quiz_scale_big.jpg

The Standard Model

In a accelerator a very small particle, eg an electron, can be accelerated by electric and magnetic fields to a very high speed. Being very small, speeds near to the speed of may be achieved. When these particles collide with a stationary target, or other fast-moving particles, a substantial amount of is released in a small space. Some of this energy may be converted into mass (E = mc2), producing showers of nuclear particles. By passing these particles through a magnetic field and observing the deflection their mass and charge can be measured. For example, an electron with low mass will be more easily deflected than its heavier cousin, the muon. A positive particle will be deflected in the opposite direction to a negative particle. Cosmic rays from outer space also contain particles, which can be studied in a similar manner.

Most matter particles, such as , and have corresponding .

These have the same rest mass as the particles but the opposite charge. With the exception of the of the electron e-, which is the e+, antiparticles are given the same symbol as the particle but with a bar over the top.

When a particle and its antiparticle meet, in most cases, they will annihilate each other and their mass is converted into energy. There are far more particles than antiparticles in the Universe, so is extremely rare.

3 The Fundamental Particles Fundamental particles are particles that cannot be divided into smaller particles. In the standard model of , there are 12 fundamental particles (called Fermions). 6 types of quarks and 6 types of leptons. These all have corresponding antiparticles. There are also 4 force carriers.

Leptons have no size and in most cases low or no mass. There are three generations of leptons, only electrons occur in ordinary mass. occur in the upper atmosphere and the tau has only been seen in experiments.

Quarks have fractional charges. The top is the most massive fundamental particle, almost 200 times the mass of a . There are also three generations. Individual quarks have never been detected. 1st 2nd 3rd 2.4 MeV/c2 1.27 GeV/c2 171.2 GeV/c2 0 MeV/c2 2/3 u 2/3 c 2/3 t 0 γ up charm top Quarks 4.8 MeV/c2 108 MeV/c2 4.2 GeV/c2 0 MeV/c2 -1/3 d -1/3 s -1/3 b g down strange bottom

<2.2 eV/c2 <0.17 MeV/c2 <15.5 MeV/c2 91.2 GV/c2

0 0 0 0 νe νµ ν 0 Force carriers electron muon τ Z neutrino neutrino tau neutrino Z boson Leptons 0.511 MeV/c2 105.7 MeV/c2 1.777 GeV/c2 80.4 GeV/c2 -1 e -1 µ -1 τ W+ electron muon tau W boson

4 Hadrons are particles made from quarks that are held together by the strong force, composite particles. This force is so strong that quarks have never been found individually. There are two types of hadron: Baryons - made of three quarks or three antiquarks Mesons - made of a quark and an antiquark. Quark Song The baryons and mesons can only have whole integer charges, 2e, e, 0, -e and -2e. There are other rules governing the joining of interactions, strangeness, spin, topness. We will not cover these in this course.

quarks quark charges total charge baryon or

uud (proton) 2/3 2/3 -1/3 +1 baryon

ūd (negative ) -2/3 -1/3 -1 meson

Ordinary matter contains only the first generation of quarks. What did the electron, Very high are needed to make hadrons of other quarks. muon and tau do when they saw the tram?

Particles experience four : strong (nuclear) force, c They ! weak (nuclear) force, gravitational force and electromagnetic force.

Strong (Nuclear) Force Gravitational Force • Electrostatic theory predicts that • See Unit 1 notes the protons in the nucleus should fly • Has infinite range apart. • Weakest of all the fundamental This does not happen so there must forces be another force present. This is known as the strong force and holds the protons together. • The strong force acts over a short range and over this short range it is stronger than the electrostatic force. • Only experienced by quarks.

Weak (Nuclear) Force Electromagnetic Force • Involved in radioactive beta decay. • Combination of the electrostatic and • Acts over a short range magnetic forces • Is weaker than the strong nuclear • Has infinite range force (hence its name) • Experienced in quark and lepton interactions 5 Grand Unification Theory Scientists are working towards a Grand Unification Theory which will link all the forces into one theory. Gravitational Force is proving more difficult to link to the other forces. For this reason the gravitational force is not included in the Standard Model. The gravitational force is relatively very weak and therefore can be ignored in terms of subatomic particles.

The sub-atomic non contact forces are explained using force carriers. The force carriers are:

Photon Gluon W boson Z boson Graviton*

Electromagnetic Strong nuclear Weak nuclear Weak nuclear Gravitational

* Gravitons are purely theoretical and have not been discovered. Beta decay

When there is beta decay a decays into a proton. (a down quark decays into http://hyperphysics.phy-astr.gsu.edu/hbase/nuclear/imgnuc/betaw.gif an up quark). This happens through the emission of a W- (weak force interaction) and an electron is forced out at high speeds. The emitted electron has less energy than theory predicts. Hence a another particle has to be emitted, due to the conservation of . This particle had to be neutral and penetrating as it did not interact with detectors. This particle was calculated to be an anti-electron neutrino. There is also another type of beta decay, known as beta +. In this process a proton decays into a neutron. A positron and neutrino are emitted. 6 HIGHER PHYSICS

2) FORCES ON CHARGED PARTICLES

Can you talk about: a) Electric fields around charged particles and between parallel plates

• Examples of patterns including single point charges, systems of two point charges and the field between parallel plates.

b) Movement of charge in an electric field, p.d. and work, electrical energy

• The relationship between potential difference, work and charge gives the definition of the volt. • Calculating the speed of a charged particle which has been accelerated in an electric field.

c) Charged particles in a

• A moving charge produces a magnetic field. • The direction of the force on a charged particle moving in a magnetic field should be described for negative and positive charges.

d) Particle accelerators

• Basic operations of particle accelerators in terms of acceleration, deflection and collision of charged particles.

7 ElectricElectric FieldsFields

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E = 25 J E = 100 J Q = 5 C E = QV Q = 2.5 C E = QV 25 = 5 x V 100 = 2.5 x V V = 5 V V = 40 V Electrical Potential Energy to Kinetic Energy

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When an electron is free toWhen move an inelectron the electricis free to fieldmove inbetween the electric two field oppositelybetween two charged oppositely metal charged plates, metal plates, the work done by the electricthe work field done onby the the electron electric field ison converted the electron tois kineticconverted energyto kinetic energyof the ofelectron the electron. .

work done on electron6&%7(+&'!(&'(!"!#$%&' gain in,/)'()'(7)'!$)#(!'!%,- kinetic energy 8 by electric field3-(!"!#$%)#(*)!"+= of electron&*(!"!#$%&' 9(: 8 1 ;<=4(>= QV = mv2 4/,')$?+! &*(#./%,! 1&$!'$)/"(+)**!%!'#! 4/55(&*(!"!#$%&' 51!!+(&*(!"!#$%&'< &'(!"!#$%&' $.%&?,.(6.)#. 2 @FA;;(D;CEI; 7,H 4(5E; magnitude of potential@;ABC(D;CE;F differenceGH !"!#$%&'()5(4&>!+< charge on electron through which : mass of electron speed of electron -1 -19 -31 ms (1.60 x 10 C) [Thiselectron equation is moved also applies to any(9.11 other x charged 10 kg) particle in an electric field]. V 0-1)#/"(2%&3"!4 [This equation also applies;*("."$/%2*(&#(3%""(/2(126"(&*()*("."$/%&$(3&".+<(= to any other charged particle0"("."$/%2*(&#()$$"."%)/"+('7(/0"(3&".+(3%21(%"#/ in an electric field]. /0%2>40()(-2/"*/&).(+&33"%"*$"(23(?@@(A<(B).$>.)/"(/0"(51!!+ 23(/0"("."$/%2*()/(/0"("*+(23(/0" )$$"."%)/&2*< Example 52%C(+2*"(2*("."$/%2* 4)&*(&*(C&*"/&$("*"%47 '7("."$/%&$(3&".+ D 23("."$/%2* ∴ (((((((((((((((E(A((((((D((((((FGH(1(6H An electron is free to move in an electric field. The electron∴ is(((((((((((((((IF

∴ (((((((((((((((6(((D F

Magnetic fields are produced by moving charges or currents in wires. In a simple bar there do not appear to be any currents but the magnetic field is generated by electrons orbiting that make up the structure of the magnet.

WARNING Current can be considered as the flow of electrons or as conventional current (the flow of positive charges). For Higher Physics you need to know how to interpret the effects of BOTH on a current carrying wire.

If a current flows through a piece of wire then a magnetic field will be produced around the wire.

The direction of the magnetic field depends on the direction of current flow.

The direction can be determined using the screw rule.

Electron Current Conventional Current

dots represent current coming out of the page

x crosses represent current going into the page

10 Forces on a current carrying wire

Electron Current A wire carrying an electric current will experience a mechanical force when placed in a magnetic field.SECTION When 2: FORCESthis ON CHARGED PARTICLES happens, the magnetic field pushes on the wire. The force of this "push" relates 3. The diagramsdirectly show to the particles intensity entering of the current a region, where there is a the strength of the magnetic field and uniform magnetic field. (X denotes magnetic field into page and • the length of the wire. denotes magnetic field out of page.)

Use the terms: You can up, visualize down,SECTION into this the2:relationship FORCES paper, ON CHARGED byout of PARTICLES the paper, left, Conventional Currentright, no changeusing the in “directionright hand to rule describe” (electron the deflection of the current) or "left hand rule" (conventional 3. particles The diagrams in theshow magneticparticles entering field. a region where there is a current). If the first finger points in the uniform magnetic field. (X denotes magnetic field into page and • SECTION 2: FORCES ON CHARGED PARTICLES direction of the magnetic field, the second denotes magnetic field out of page.)magnetic field magnetic field magneticfinger field in the direction of the current, then Use the terms:the thumb up, down, represents into the paper, the direction out of the of paper,the left, 3. The diagrams show particles entering a region where there is a right, no change in directionforce thrust to describe (or motion). the deflection of the particles in the magnetic field. uniform magnetic field. (X denotes magnetic field into page and • proton electron alpha (a) denotes magnetic field out ofparticle page.) magnetic field magnetic field magnetic field (b) (c) SECTION 2: FORCES ON CHARGED PARTICLES Use the terms: up, down, into the paper, out of the paper, left, right, no change in direction to describe the deflection of the proton electron alpha magnetic(a) field particles in the magneticparticle protonfield. 3. The diagrams show particlesConversely entering if a we region have wherea magnetic there field is a acting on a moving charge it will(c) neutron (b) uniform magnetic field. experience(X denotes a magneticforce. However, field into if the page charge and travels • parallel to the magnetic field, electron magnetic field magnetic field magnetic field denotes magnetic field out of page.) it will not experiencemagnetic fieldan additional force. proton neutron magnetic field Use the terms: up, down, intoThe the direction paper, outof the of force the paper,is determined left, usingelectron the same “hand ruleʼs”. (d) proton magnetic field alpha right, no change in direction to describe the deflection of the (e) electron magnetic field particle The speed of the charge will not change(d) , only the direction of motion changes.(a) (f) particles in the magnetic field. (e) magnetic field (c) electron (f) (b) magnetic field magnetic field magnetic field electron x x x x x x x x x x x x xmagneticx x xx x fieldx x proton xx x xx x xx x x x x x x xx x x x xx x xx x xx x x x x x x proton x x x x x neutronx x x x x xx protonx x x proton electron xx alphax x x x xx x x x x x x xx x x x xx x xx x xx x electron (a) particle magnetic fieldmagnetic field magnetic field magnetic field (h) (b) (c) (g) (h) magnetic field (g) (d) (e) magnetic field The electron will curve to the No change in direction as a magnetic field The electron will curve out of 4. Anproton electron enters a region of space where there is a uniform (f) the page. 4. Anmagnetic electronright field. enters As it enters a region the field neutralof the space velocity particle. where of the there electron is a uniform neutron is at right angles to the magnetic field lines. magnetic field. As it enters the field theelectron velocity of the electron electron The energy of the electron does not change although it x x x x x isaccelerates at right inangles the field. to the magneticx xfieldx lines.x x x x x x x magnetic field TheUse energyyour knowledge of the of electronphysics to explaindoesx notthisx effect.changex x x although it x x x x x (d) accelerates in the field. x x x x x x x x x x proton (e) magnetic field x x x x x x x x x x Use your knowledge of physics xto explainx x x thisx effect. (f) magnetic field magnetic field electron PARTICLES AND WAVES (H, PHYSICS) 11 (h) x x x x x (g) x x x x x x x x x x x x x x x x x x x x 11 x x x x x x x x x x proton 4. An electron entersPARTICLES a regionAND WAVES of (H, spacePHYSICS) 11where there is a uniform x x x x x x x x x x x x x x x magnetic field. As it enters the field the velocity of the electron magnetic field magnetic field is at right angles to the magnetic field lines. (h) (g) The energy of the electron does not change although it accelerates in the field. Use your knowledge of physics to explain this effect. 4. An electron enters a region of space where there is a uniform magnetic field. As it enters the field the velocity of the electron is at right angles to the magnetic field lines. The energy of the electron does not change although it accelerates in the field. PARTICLES AND WAVES (H, PHYSICS) 11 Use your knowledge of physics to explain this effect.

PARTICLES AND WAVES (H, PHYSICS) 11 ACCELERATORS

Beams of charged particles experience a deflection by both electric and magnetic fields. This can be used to accelerate particles, cause collisions and investigate the particles and energies produced. In a cyclotron, are injected at a point near the centre. A potential difference between the ʻdeeʼ shaped electrodes accelerates the particles. A magnetic field causes the particles to move in a circular path. When the particle crosses from one dee to another it accelerates. After each acceleration the particle moves to a slightly larger orbit. When it reaches the outer edge of the cyclotron the is extracted and used in other experiments.

Linear accelerator (LINAC) Charged particles are accelerated in a pipe through a series of electrodes by an alternating . The beam of particles is then directed at a target or into a . http://www.fi.edu/guide/jones/synchrotron.gif

Synchrotron This is similar to a linear accelerator, bent into a ring so the charged particles can be given more energy each time they go round. keep the particles in a curved path. As the speed increases, the magnetic field strength is increased. As the speed increases and relativistic effect cause the mass of the particles to increase, a larger force is needed to accelerate them and keep them in a circular path.

CERN CERN is the European particle physics laboratory, it is near Geneva in Switzerland and was established in 1954. 20 European countries collaborated in funding and running CERN. About 3000 people work there, with are many visiting scientists that represent over 80 nations. They have a number of accelerators and a number of detectors. LHC, ATLAS, ALICE, CMS and TOTEM.

Scientists working at CERN have a large amount of information to send to each other. In 1989 Tim Berners Lee wrote a proposal for an information system, and by the end of 1990 the World- Wide Web was up and running.

CERN

12 HIGHER PHYSICS

3 NUCLEAR REACTIONS

Can you talk about:

Fission and fusion

• Nuclear equations to describe and fission and fusion reactions. • Mass and energy equivalence, including calculations. • Coolant and containment issues in reactors.

13

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OUR PRESENT DAY MODEL OF THE ATOM

Nucleus. Contains protons (+ charge) and neutrons (0 charge), so has overall + charge.

electrons (- charge) circle around nucleus

mass number (represents the total number of protons plus neutrons in the nucleus) "#$ chemical The symbol for an atom is often written in this form: symbol OUR PRESENT DAY MODEL OF THE ATOM%"! atomic number (represents the number of protons in the Nucleus. Contains protons (+ charge) and nucleus) neutronsMODEL (0 charge), so hasOF overall THE + charge. ATOM build an To find the number of neutrons in an atom, we subtract the atomic number from the mass number, Nucleus. Contains protons (+ charge) and atom e.g., for the atom above: neutronsNumber (0 charge),of neutrons so has overall = mass + charge. number - atomic number electrons (- charge) circle around nucleus = 235 - 92 = 143. electrons (- charge) The symbol for an atom is often written in &'()*+,(-.(,*/(0123/4(56(745,50.circle around nucleus+08(,*/(0123/4(56(0/1,450. -0(,*/./(+,52.9(( RADIOACTIVE DECAYthis form: RADIOACTIVEmass number DECAY(represents From Standard Grade Physics, you know that <=three tymasspes of number radioactivity (represents is emitted from atoms during&=> "# the total number of protons&=& radioactiveFrom Standard decay - Gradealpha Physics, particles you, beta know particles that threeand the ty gammatotalpes numberof radioactivity rays of protons. is emitted from atoms during ;0plus neutrons in the nucleus) ?+ @/ radioactive decay &&- alpha:+ particlesRADIOACTIVE, beta particles#> plusand neutrons DECAYgamma in the rays nucleus)$<. $= Complete this table: "#$ chemical FromComplete Standard this Gradetable: Physics, you know that three types of radioactivity is emitted from atoms during TheType symbol of for an atom Symbol is often written What in itthis is form: What stops it Amount of ionisationsymbol radioactiveType of radiationdecay - alphaSymbol particles , beta WhatRADIOACTIVE particles it is and gamma What raysDECAY .stops it Amount! of ionisation Complete this table: %" atomicatomic number number(represents (represents From Standard Grade Physics, you know thatthe three number types of protonsof radioactivity in the is emitted from atoms during Type of radiation Symbol What it is the number What of protons stops it in the Amount of ionisation !!!!"#$%" radioactive decay - alpha particles, beta particlesnucleus) and gamma rays. !!!!"#$%" nucleus) To find the numberComplete of this neutrons table: in an atom, we subtract the atomic number from the mass number!!!!"#$%", e.g.,Type for ofthe radiation atom above:Symbol Number What of neutronsit is ! = What mass stops number it -Amount atomic of numberionisation To find!!!!!!!!!!! the number of neutrons in an atom, we subtract the atomic= 235 number- 92 = 143.from the mass number, e.g.,!!!! for&'(" the atom above: Number of neutrons = mass number - atomic number AtomsAtoms which which !!!!have"#$%" havethe same the sameatomicatomic number number but differentbut different mass numbersmass numbers are knownare asknown as , !!!! &'(" = 235 - 92 = 143. isotopese.g., , uraniume.g., has isotopes: has isotopes: !!!!&'(" "#$ "#A +08 &'()*+,(-.(,*/(0123/4(56(745,50. +08(,*/(0123/4(56(0/1,450.%" ! %" ! -0(,*/./(+,52.9(( !!!)"**" !!!!&'(" !!!)"**""'B+'(C5D(2+0E(745,50.(+08(0/1,450.(+4/(74/./0,(-0(<= &=& /+F*(14+0-12(-.5,57/9&=> !!!"#)"**" NUCLEAR DECAY :+ #> ;0 $< ?+ $= @/ From&& Intermediate 2 Physics, you know that three types of radioactivity may be emitted from atomic nuclei!!!)"**" during radioactive decay - alpha particles, beta particles and gamma rays. "#$%"!+',"- &'("!+',"- alpha"#$%"!+',"-"#$%"!+',"- decay &'("!+',"-beta&'("!+',"- decay Alpha decay takes place when an alpha particle Beta decay takes place when a neutron in the AlphaAlpha decay decaytakes takes place place when when"#$%"!+',"- an alphaan alphaparticle BetaBeta decay decaytakestakes place place&'("!+',"- when when a neutron a neutronin the in the (consistingAlpha decayof B3'(G5/.(/+F*(14+0-12(-.5,57/(*+H/I2 protonstakes place plus when 2 neutrons an alpha )particle is nucleusBeta splitsdecay up takes into placea proton whenand a neutronan electron in . particle (consisting of 2 protons plus 2 nucleusnucleussplitssplits up intoup intoa proton a protonand anand electron an electron. . (consisting(consisting of of2 2protons protons plusplus 2 neutrons) )is is The theproton nucleusBetastays decay splits intakes the up place nucleus into when a proton a(so neutron the and atomic inan the ejected fromAlphaB-'(,*/(.+2/(0123/4(56(745,50.9JJJJ((B--'(,*/(.+2/( an decay atom'stakes nucleus. place when an alpha particleThe proton stays in the nucleus0123/4(56(0/1,450.9JJJJ(so the atomic neutronsejectedejected) is ejected from from an anfrom atom's atom's an atom's nucleus. nucleus. Theelectron protonnucleus. Thestayssplits proton up in into the staysa nucleusproton in theand( so nucleusan theelectron atomic . (consisting of 2 protons plus 2 neutrons)number isnumber increases by by 1) 1 while) while the the electron electronis is An alphaAnAn particlealpha alpha particle particleis representedis representedis represented by theby the symbol:by symbol: the (sonumber theThe atomic protonincreases numberstays byin theincreases 1) nucleuswhile the (byso electron 1 the) while atomic is An alpha particle is representedejected from an by atom's the symbol:nucleus. ejectedejected from thethe atom's atom's nucleus nucleusas aas beta a beta symbol: ejectedthe 45 numberelectron from increases theis ejected atom's by 1 )from nucleuswhile thethe electronatom'sas a beta is An #alpha #particle is represented by the symbol: particleparticle. . !"# !" ejectednucleus from as the particlea atom's beta particlenucleus. as. a beta Atoms which have $the same$!" atomic# number but differentAA beta beta particlemass isnumbersis represented representedparticleare by known. bythe thesymbol: assymbol: isotopes, $ !" A Abeta particle is isrepresented represented by by the the symbol: symbol: e.g., uraniumA different has isotopes: atom is created $as a result: A beta particle is represented by the symbol: A differentA different atom atom is created is created as aas result: a result: "#$ "#A % A different atomA different is created atom asis created a result: as a result: +08 % ! %" ! &' ""%% # %" &' "" $() $(# # A different atom is created&'&' as a result: $()$() $()$(# $(#+ # # A different atom is created as a result: "'B+'(C5D(2+0E(745,50.(+08(0/1,450.(+4/(74/./0,(-0(*$+ $(#*%,-+ +$!"+ AA different differentA different atom /+F*(14+0-12(-.5,57/9atom atom is is created iscreated created as asas a a a result:result: result: *$+original (parent) *$*%+,-new (daughter)*%$,-!" emitted$!"$(# $(# original*$ (parent)+ originalnew (parent) *% (daughter),-new (daughter) $emitted!" emitted % original (parent)atom new (daughter) atom alpha emitted particle $(# $(# $(#$(# + % atom atom alpha particle$(# $(# + % atom atom alpha particle *'./ *$+ +&'"% atom atom alpha particle original (parent)*'./ new (daughter)*$+ emitted+&'" TheThe mass mass number number ofof the new new (daughter) (daughter) atom atom is *'./original (parent) *$new+ (daughter) &' emitted" The mass number of the new (daughter) atomoriginal is *' atom (parent)./ new atom (daughter)*$+beta particle emitted&'" ______than the original (parent) atom beta particle The ismass four number less than____ of thethe ______new original (daughter) than (parent). the original atom The (parent) is atomoriginal (parent) atom new (daughter) atom emitted The andmass the number atomic number of the newis ____ (daughter) ______. atom is atom atom beta particle ______thanand the the atomic original number (parent) is ____ atom ______. atom atom beta particle ____atomicB3'(G5/.(/+F*(14+0-12(-.5,57/(*+H/I ______number is than two the less original than the (parent) original. atom TheThe mass massThe number numbermass number of of the the ofnew the new (daughter) new (daughter) (daughter) atom atom atomis is and the atomic number is ______. ______the original (parent) atom and theB-'(,*/(.+2/(0123/4(56(745,50.9JJJJ((B--'(,*/(.+2/( atomic number is ______. Theis the mass ____same number ______as the0123/4(56(0/1,450.9JJJJ of ____originalthe new the (parent) original(daughter) (parent) atom atom and atom is andThe the mass andatomic the number numberatomic number ofis ____the is new ______.____ (daughter) ______. atom is the atomic number is one bigger. ______the the original original (parent) (parent) atom atom TOTAL OF MASSTOTAL NUMBERS OF MASS ON NUMBERS LEFT OF ONARROW LEFT OF= ______ARROW = ______andTOTAL the OF atomicTOTAL MASS OF NUMBERS MASSnumber NUMBERS ON is LEFT ____ ON OF LEFT ARROW ______. OF ARROW = ______= ______45 and____ the atomic number is ______. ______Gamma rays are photons____ of electromagnetic______energy - They are not particles__ __. TOTAL OF gammaMASS NUMBERS ON LEFT OF ARROW = ______TOTAL OF MASS NUMBERSTOTAL OF ATOMIC ON LEFT NUMBERS OF ARROW ON LEFT = OF ______ARROW =TOTAL ______OF MASS NUMBERS ON LEFT OF ARROW = ______TOTAL OF ATOMIC NUMBERSWhen ON gamma LEFT OF ARROWrays are = ______ejectedTOTAL fromTOTAL OF an TOTAL OFATOMIC atom's MASS OF NUMBERSATOMIC NUMBERS nucleus NUMBERS ON ,ON LEFTthis ONLEFT OFdoes LEFT ARROW OF OF notARROW ARROW = change ______= ______decay the mass number or atomic____ number______of ______the atom. It does however change the______energy state Gammaof the nucleus. rays are electromagnetic energy - They are not particles. When TOTAL OF ATOMIC NUMBERS ON GammaLEFT OF raysARROWare = electromagnetic ______TOTAL15 OFenergy ATOMIC- They NUMBERS are not ON particles LEFT OF. ARROWWhen = ______TOTAL OF ATOMIC NUMBERS ON LEFT OFgamma ARROW rays = ______are ejectedTOTAL from anOF atom'sATOMIC nucleus NUMBERS (along ON with LEFT alph OFa ARROWand beta = ______)"**"!+',"-gamma rays are ejected____ from______an atom's nucleus (along with alpha and beta ______)"**"!+',"- particles), this does____ not change______the mass number or atomic number of the atom. __ particles), this does not change the mass number or atomic number of the atom. GammaGamma rays raysareare electromagnetic electromagnetic 46energy energy- They- They are are not not particles particles. When. When 46 )"**"!+',"-)"**"!+',"- gammagamma rays raysareare ejected ejected from from an anatom's atom's nucleus nucleus (along (along with with alph alpha anda and beta beta particles),particles), this this does does not notchange change the the mass mass number number or atomicor atomic numb number erof ofthe the atom atom. .

46 46

NUCLEAR FISSION NUCLEARNUCLEAR FISSION FISSION In nuclear fission, a large splits into 2 smaller nuclei and several neutrons. In nuclear fissionIn ,nuclear a large atomicfission ,nucleus a large atomicsplits into nucleus 2 smallersplits nuclei into 2 andsmaller several nuclei neutronsand several. neutrons. The smallerChain nuclei and neutronsNUCLEARNUCLEARNUCLEARproduced gain FISSION large FISSIONFISSION amounts of kinetic energy. JeT The smaller nucleiThereaction andsmaller neutrons nucleiproducedand neutrons gain largeproduced amounts gain oflarge kinetic amounts energy. of kinetic energy. In nuclear fission, a large atomicNUCLEAR nucleus splits FISSION into 2 smaller nuclei and several neutrons. In nuclearIn nuclearfissionfission, a large, a large atomic atomic nucleus nucleussplitssplits into 2into smaller 2 smaller nuclei nucleiand severaland several neutrons neutrons. . TheThe smallersmaller nucleinuclei andand neutronsneutrons producedproduced gaingain largelarge amountsamounts ofof kinetickinetic energy.energy. Fission mayIn Thenuclearbe either: smaller fission nuclei, a largeand atomicneutrons nucleusproduced splits gain into large 2 smaller amounts nuclei of andkinetic sometimes energy. several Fission may be Fissioneither:neutrons may .be The either: smaller nuclei and neutrons that are produced gain large amounts of kinetic (a) Spontaneous(a)Fission Spontaneous may be either: energy. (a) SpontaneousFissionFissionFission may maybe may either: be be either: either: The large atomic nucleus splits up by itself at random - There is no "outside influence". The large atomicThe (a)nucleus(a) large SpontaneousSpontaneous atomicsplits up nucleus by itselfsplits at random up by -itself There at israndom no "outside - There influence" is no "outside. influence". For(a) example: Spontaneous(a) Spontaneous For example: The For large example: atomic nucleus splits up by itself at random - There is no "outside influence". The ThelargeThe large atomiclarge atomic atomic nucleus nucleus nucleussplitssplits upsplits by up upitself by by itself atitself random at at random random - There -- ThereThere is no is is"outside nono "outside influence" influence"influence". . ForFor example:example:*+',$"+&(-./"#%/*$%) 0")-+**$'"#%/*$. !"#$%&'(#) For!*+',$"+&(-./"#%/*$%) example:For example:*+',$"+&(-./"#%/*$%)0")-+**$'"#%/*$. 0")-+**$'"#%/*$.!"#$%&'(#) !"#$%&'(#)

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!"#$%#$%&'%()&*+,(%-.%&%'/0,(&1This is an example of a nuclear fission.#$$#-' reaction:1(&02#-'3 235 1 134 98 1 U + n Te + Zr + 4 n 92 0 52 40 0

3.901 x 10-25 kg 0.017 x 10-25 kg 2.221 x 10-25 kg 1.626 x 10-25 kg 0.017 x 10-25 kg The mass of each species taking part in the reaction is shown in blue. !"(%*&$$ -.%(&0"%$+(0#($%2&4#'5%+&12%#'%2"(%1(&02#-'%#$%$"-6'%#'%7,/(8 (a) Describe what happens in a nuclear (b) Explain whether the above nuclear 9&:%;($01#7(%6"&2%"&++('$%#'%&fission reaction: fission97:%=)+,&#'%6"(2"(1%2"(%&7->( reaction is "spontaneous" or A'/0,(&1 larger atomic.#$$#-' nucleus1(&02#-'3 splints into "induced":'/0,(&1 .#$$#-' 1(&02#-'%#$ <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<2 smaller nuclei, several neutrons Induced.?$+-'2&'(-/$?%-1%?#'@/0(@?3 A neutron is fired at the <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

(d) Calculate the total mass of the species on the right of the arrow (the products): 90: 2.221x10-25 + 1.626x10-25 + (4 x 0.017x10-25 ) = 3.915x10-25 kg A&,0/,&2( 2"(%2-2&, *&$$ (e)-.%2"( Calculate the lost mass when this (f) Calculate the kinetic energy gained $+(0#($%-'nuclear fission reaction happens once: by the products when this nuclear 2"(%,(.2 -. fission reaction happens once: 2"(%&11-6 92"(3.918x10-25 - 3.915x10-25 = 0.003-25 kg E = mc2 1(&02&'2$:3 E = 0.003x10-25 x (3x108)2 E = 2.7x10-11 J

!"#$%#$%&'%()&*+,(%-.%&%'/0,(&1 ./$#-' 1(&02#-'3 9@: This is an example of a nuclear fusion reaction: A&,0/,&2( 2 2 3 1 2"(%2-2&, *&$$ -.%2"( H + H He + n $+(0#($%-'1 1 2 0 2"(%1#5"23.342-. x 10-27 kg 3.342 x 10-27 kg 5.004 x 10-27 kg 1.674 x 10-27 kg 2"(%&11-6 The mass of each species taking part in the reaction is shown in blue. !"(%*&$$92"( -.%(&0"%$+(0#($%2&4#'5%+&12%#'%2"(%1(&02#-'%#$%$"-6'%#'%7,/(8 +1-@/02$:3 Calculate the kinetic energy gained by the products when this nuclear fusion reaction 9&:%;($01#7(%6"&2%"&++('$%#'%&happens once. 97:%=2&2(%6"(1(%'/0,(&1 ./$#-' 9(:%A&,0/,&2(%2"(%,-$2'/0,(&1 ./$#-' 1(&02#-'3*&$$ 6"('%2"#$ 9.:%A&,0/,&2(%2"(%4#'(2#01(&02#-'$%2&4(%+,&0(3('(15B 5&#'(@ lost mass = ( 3.342x10-27 + 3.342x10-27 ) - (5.004x10-27 + 1.674x10-27 ) '/0,(&1%.#$$#-'%1(&02#-'%"&++('$%-'0(3 7B%2"(%+1-@/02$%6"('%2"#$%'/0,(&1 <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

49 90: >&,0/,&2( 2"(%2-2&, *&$$ -.%2"( $+(0#($%-' 2"(%,(.2 -. 2"(%&11-6 92"( 1(&02&'2$:3

9@: >&,0/,&2( 2"(%2-2&, *&$$ -.%2"( $+(0#($%-' 2"(%1#5"2 -. 2"(%&11-6 92"( +1-@/02$:3

9(:%>&,0/,&2(%2"(%,-$2 *&$$ 6"('%2"#$ 9.:%>&,0/,&2(%2"(%4#'(2#0 ('(15? 5&#'(@ '/0,(&1%./$#-'%1(&02#-'%"&++('$%-'0(3 7?%2"(%+1-@/02$%6"('%2"#$%'/0,(&1 ./$#-'%1(&02#-' "&++('$%-'0(3

50 TUTORIAL QUESTIONS

Section 1: The standard model

Orders of magnitude

1. The diagram shows a simple model of the atom.

Match each of the letters A, B, C and D with the correct word from the list below.

electron neutron nucleus proton

2. In the following table the numbers or words represented by the letters A, B, C, D, E, F and G are missing.

Order of magnitude/m Object 10−15 A 10−14 B 10−10 Diameter of atom 10−4 C 100 D 103 E 107 Diameter of Earth 109 F 1013 Diameter of solar system 1021 G Match each letter with the correct words from the list below.

diameter of nucleus diameter of proton diameter of Sun distance to nearest galaxy height of Ben Nevis size of dust particle your height

18 The standard model of fundamental particles and interactions

1. Name the particles represented by the following symbols.

(a) p (b) (c) e (d)

(e) n (f) (g) v (h)

M 2. A particle can be represented by a symbol A X where M represents the mass number, A the atomic number and X identifies the type of particle, for example a proton can be

represented by . Give the symbols, in this form, for the following particles.

(a) (b) e €(c) (d) n (e)

3. Copy and complete the table by placing the fermions in the list below in the correct column of the table.

bottom charm down electron electron neutrino muon muon neutrino strange tau tau neutrino top up

Quarks Leptons

4. (a) State the difference between a hadron and a lepton in terms of the type of force experienced by each particle. (b) Give one example of a hadron and one example of a lepton.

19 5. Information on the sign and charge relative to proton charge of six types of quarks (and their corresponding antiquarks) is shown in the table.

Quark name Charge relative to Antiquark name Charge relative to size of proton size of proton charge charge up +2/3 antiup –2/3 charm +2/3 anticharm –2/3 top +2/3 antitop –2/3 down –1/3 antidown +1/3 strange –1/3 antistrange +1/3 bottom –1/3 antibottom +1/3

Calculate the charge of the following combinations of quarks:

(a) two up quarks and one down quark (b) one up quark and two down quarks (c) two antiup quarks and one antidown quark (d) one antiup quark and two antidown quarks.

6. Neutrons and protons are considered to be composed of quarks.

(a) How many quarks are in each neutron and in each proton? (b) Comment briefly on the different composition of the neutron and proton.

7. (a) Briefly state any differences between the ‘strong’ and ‘weak’ nuclear forces. (b) Give an example of a particle decay associated with the weak nuclear force. (c) Which of the two forces, strong and weak, acts over the greater distance?

20 Section 2: Forces on charged particles

Electric fields

1. Draw the electric field pattern for the following point charges and pair of charges:

(a) (b) (c)

2. Describe the motion of the small positive test charges in each of the following fields.

(a) (b)

(c) (d)

3. An electron volt (eV) is a unit of energy. It represents the change in potential energy of an electron that moves through a potential difference of 1 V (the size of the charge on an electron is 1·6 × 10−19 C). What is the equivalent energy of 1 eV in joules?

4. An electron has energy of 5 MeV. Calculate its energy in joules.

5. The diagram shows an electron accelerates between two parallel conducting plates A and B.

The p.d. between the plates is 500 V. (mass of electron = 9·1 × 10−31 kg charge on electron = 1·6 × 10−19 C)

(a) Calculate the electrical work done in moving the electron from plate A to plate B. (b) How much kinetic energy has the electron gained in moving from A to B? (c) What is the speed of the electron just before it reaches plate B?

21 6. Electrons are ‘fired’ from an at a screen.

The p.d. across the electron gun is 2000 V. The electron gun and screen are in a vacuum. After leaving the positive plate the electrons travel at a constant speed to the screen. Calculate the speed of the electrons just before they hit the screen.

7. A proton is accelerated from rest across a p.d. of 400 V. Calculate the increase in speed of the proton.

8. In an X-ray tube electrons forming a beam are accelerated from rest and strike a metal target. The metal then emits X-rays. The electrons are accelerated across a p.d. of 25 kV. The beam of electrons forms a current of 3·0 mA.

(a) (i) Calculate the kinetic energy of each electron just before it hits the target. (ii) Calculate the speed of an electron just before it hits the target. (iii) Find the number of electrons hitting the target each second. (mass of electron = 9·1 × 10−31 kg charge on electron = 1·6 × 10−19 C) (b) What happens to the kinetic energy of the electrons?

9. Sketch the paths which

(a) an alpha-particle (b) a beta-particle (c) a neutron

would follow if each particle, with the same velocity, enters the electric fields shown in the diagrams.

22 Charged particles in a magnetic field

1. An electron travelling with a constant velocity enters a region where there is a uniform magnetic field. There is no change in the velocity of the electron. What information does this give about the magnetic field?

2. The diagram shows a beam of electrons as it enters the magnetic field between two . The electrons will:

A be deflected to the left (towards the N pole) B be deflected to the right (towards the S pole) C be deflected upwards D be deflected downwards E have their speed increased without any change in direction.

3. The diagrams show particles entering a region where there is a uniform magnetic field. (X denotes magnetic field into page and • denotes magnetic field out of page.)

Use the terms: up, down, into the paper, out of the paper, left, right, no change in direction to describe the deflection of the particles in the magnetic field.

magnetic field magnetic field magnetic field

proton electron alpha

(b) (c)

magnetic field proton neutron electron magnetic field (d) (e) magnetic field (f) electron x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x proton x x x x x x x x x x x x x x x magnetic field magnetic field (h) (g)

4. An electron enters a region of space where there is a uniform magnetic field. As it enters the field the velocity of the electron is at right angles to the magnetic field lines. The energy of the electron does not change although it accelerates in the field. Use your knowledge of physics to explain this effect.

23 Particle accelerators

In the following questions, when required, use the following data:

Charge on electron = –1·60 × 10−19 C Mass of electron = 9·11 × 10−31 kg Charge on proton = 1·60 × 10−19 C Mass of proton = 1·67 × 10−27 kg

1. In an evacuated tube, an electron initially at rest is accelerated through a p.d. of 500 V.

(a) Calculate, in joules, the amount of work done in accelerating the electron. (b) How much kinetic energy has the electron gained? (c) Calculate the final speed of the electron.

2. In an electron gun, electrons in an evacuated tube are accelerated from rest through a potential difference of 250 V.

(a) Calculate the energy gained by an electron. (b) Calculate the final speed of the electron.

3. Electrons in an evacuated tube are ‘fired’ from an electron gun at a screen. The p.d. between the cathode and the anode of the gun is 2000 V. After leaving the anode, the electrons travel at a constant speed to the screen. Calculate the maximum speed at which the electrons will hit the screen.

4. A proton, initially at rest, in an evacuated tube is accelerated between two charged plates A and B. It moves from A, where the potential is 10 kV, to B, where the potential is zero. Calculate the speed of the proton at B.

5. A linear accelerator is used to accelerate a beam of electrons, initially at rest, to high speed in an evacuated container. The high- speed electrons then collide with a stationary target. The accelerator operates at 2·5 kV and the electron beam current is 3 mA.

(a) Calculate the gain in kinetic energy of each electron. (b) Calculate the speed of impact of each electron as it hits the target. (c) Calculate the number of electrons arriving at the target each second. (d) Give a reason for accelerating particles to high speed and allowing them to collide with a target.

6. The power output of an oscilloscope (cathode-ray tube) is estimated to be 30 W. The potential difference between the cathode and the anode in the evacuated tube is 15 kV.

(a) Estimate the number of electrons striking the screen per second. (b) Calculate the speed of an electron just before it strikes the screen, assuming that it starts from rest and that its mass remains constant.

24 7. In an oscilloscope electrons are accelerated between a cathode and an anode and then travel at constant speed towards a screen. A p.d. of 1000 V is maintained between the cathode and anode. The distance between the cathode and anode is 5·0 × 10−2 m. The electrons are at rest at the cathode and attain a speed of 1·87 × 107 m s−1 on reaching the anode. The tube is evacuated.

(a) (i) Calculate the work done in accelerating an electron from the cathode to the anode. (ii) Show that the average force on the electron in the electric field is 3·20 × 10−15 N. (iii) Calculate the average acceleration of an electron while travelling from the cathode to the anode. (iv) Calculate the time taken for an electron to travel from cathode to anode. (v) Beyond the anode the electric field is zero. The anode to screen distance is 0·12 m. Calculate the time taken for an electron to travel from the anode to the screen.

(b) Another oscilloscope has the same voltage but a greater distance between cathode and anode. (i) Would the speed of the electrons be higher, lower or remain at 1·87 × 107 m s−1? Explain your answer. (ii) Would the time taken for an electron to travel from cathode to anode be increased, decreased or stay the same as in (a) (iv)? Explain your answer.

8. In an X-ray tube a beam of electrons, initially at rest, is accelerated through a potential difference of 25 kV. The electron beam then collides with a stationary target. The electron beam current is 5 mA.

(a) Calculate the kinetic energy of each electron as it hits the target. (b) Calculate the speed of the electrons at the moment of impact with the target assuming that the electron mass remains constant. (c) Calculate the number of electrons hitting the target each second. (d) What happens to the kinetic energy of the electrons?

9. On the same diagram shown below sketch the paths that 10. (a) an electron, (b) a proton and (c) a neutron would follow if each particle entered the given electric fields with the same velocity.

+ + + + + + + + + + +

Path of particles

− − − − − − − − − − −

25 10. In the following examples identify the charge of particle (positive or negative) which is rotating in a uniform magnetic field. (X denotes magnetic field into page and • denotes magnetic field out of page.)

X X X X

X X X X (a) X X X X

X X X X (a) (b)

X X X X

X X X X

X X X X

X X X X (c) (d)

26 11. In the following descriptions of particle accelerators, some words and phrases have been replaced by the letters A to R.

In a linear accelerator bunches of charged particles are accelerated by a series of ____A____. The final energy of the particles is limited by the length of the accelerator.

This type of accelerator is used in ____B____ experiments. In a cyclotron the charged particles are accelerated by ____C____. The particles travel

in a ____D____ as a result of a ____E____, which is ____F____ to the spiral. The radius of the spiral increases as the energy of the particles ____G____. The diameter of

the cyclotron is limited by the ____H____ of the magnet. The resultant energy of the particles is limited by the diameter of the cyclotron and by ____I____.

This type of accelerator is used in ____J____ experiments. In a synchrotron bunches of charged particles travel in a ____K____ as a result of C

shaped magnets whose strength ____L____. The particles are accelerated by ____M____. As the energy of the particles increases the strength of the magnetic field

is ____N____ to maintain the radius of the path of the particles. In synchrotron accelerators the particles can have, in theory, an unlimited series of accelerations as the

particles can transit indefinitely around the ring. There will be a limit caused by ____O____.

In this type of accelerator particles with ____P____ mass and ____Q____ charge can circulate in opposite directions at the same time before colliding. This increases the

energy of impact. This type of accelerator is used in ____R____ experiments.

Letter List of replacement word or phrase A, C, E, M constant magnetic field, alternating magnetic fields, alternating electric fields, constant electric fields B, J, R colliding-beam, fixed-target D, K spiral of decreasing radius, spiral of increasing radius, circular path of fixed radius F perpendicular, parallel G decreases, increases H physical size, strength I, O gravitational effects, relativistic effects L can be varied, is constant N decreased, increased P, Q the same, different

27 Section 3: Nuclear reactions

Fission and fusion

1. The following is a list of atomic numbers:

(a) 6 (b) 25 (c) 47 (d) 80 (e) 86 (f) 92

Use a periodic table to identify the elements that have these atomic numbers.

2. The list shows the symbols for six different isotopes.

(i) (ii) (iii) (iv) (v) (vi)

For each of the isotopes state:

(a) the number of protons (b) the number of neutrons.

3. The incomplete statements below illustrate four nuclear reactions.

Identify the missing particles or nuclides represented by the letters A, B, C and D.

4. Part of a radioactive decay series is represented below:

Identify the particle emitted at each stage of the decay. Such a series does not always give a complete picture of the emitted by each nucleus. Give an explanation why the picture is incomplete.

28 5. For a particular sample 8 × 107 disintegrations take place in 40 s. Calculate the activity of the source.

6. How much energy is released when the following ‘decreases’ in mass occur in various fission reactions?

(a) 3·25 × 10−28 kg (b) 2·01 × 10−28 kg (c) 1·62 × 10−28 kg (d) 2·85 × 10−28 kg

7. The following statement represents a involving the release of energy.

The masses of these particles are given below.

Mass of = 5·00890 × 10−27 kg

Mass of = 3·34441 × 10−27 kg

Mass of = 6·64632 × 10−27 kg

Mass of = 1·67490 × 10−27 kg

(a) Calculate the decrease in mass that occurs when this reaction takes place. (b) Calculate the energy released in this reaction. (c) What is the name given to this type of nuclear reaction? (d) Calculate the number of reactions required each second to produce a power of 25 MW.

8. can undergo the nuclear reaction represented by the statement below:

The masses of the nuclei and particles involved in the reaction are as follows.

Particle n Pu Te Mo

Mass/kg 1·675 × 10−27 396·741 × 10−27 227·420 × 10−27 165·809 × 10−27

(a) What kind of reaction is represented by the statement? (b) State the mass number and atomic number of the nuclide Te in the reaction. (c) Calculate the decrease in mass that occurs in this reaction. (d) Calculate the energy released in this reaction.

29 Solutions Section 1: The standard model Orders of magnitude

1. A= electron; B = proton; C = nucleus; D = neutron

2. A = diameter of proton; B = diameter of nucleus; C = size of dust particle; D = your height; E = height of Ben Nevis; F = diameter of Sun; G = distance to nearest galaxy

The standard model of fundamental particles and interactions

1. (a) proton (b) (c) electron (d) positron (e) neutron (f) (g) neutrino (f) antineutrino

2. (a) (b) (c) (d) (e)

3. Quarks: bottom, charm, down, strange, top, up Leptons: electron, electron neutrino, muon, muon neutrino, tau, tau neutrino

4. (a) Leptons are particles that are acted on by the weak nuclear force but not by the strong nuclear force. Hadrons are particles that are acted on by the weak and strong nuclear force. (b) Leptons – any one of electron, electron neutrino, muon, muon neutrino, tau and tau neutrino. Hadron – any one of up, down, charm, strange, top and bottom.

5. (a) +e (b) 0 (c) −e (d) 0

6. (a) 3 (b) For the neutron the three quarks must give a charge of zero. For the proton the three quarks must give a charge of +e.

7. (a) Strong force has a range of less than 10−14 m; weak force has a range of less than 10−17 m. (b) Beta decay (c) Strong force.

Section 2: Forces on charged particles Electric fields

3. 1·6 × 10−19 J

4. 8·0 × 10−13 J

5. (a) 8·0 × 10−17 J (b) 8·0 ×10−17 J (c) 1·3 × 107 m s −1 ¶

6. 2·65 × 107 m s −1

7. 2·76 × 105 m s −1

8. (a) (i) 4·0 × 1015 J (ii) 9·4 × 107 m s−1 (iii) 1·9 × 1016

30 Charged particles in a magnetic field

1. Magnetic field is in the same plane and in the same or opposite direction to the velocity of the electron.

2. C: be deflected upwards

3. (a) no change in direction (b) out of the paper (c) into the paper (d) no change in direction (e) up (f) left (g) left (h) down

Particle accelerators

1. (a) 8 × 10−17 J (b) 8 × 10−17 J (c) 1·33 × 107 m s −1

2. (a) 4 × 10−17 J (b) 9·37 × 106 m s −1

3. 2·65 × 107 m s −1

4. 1·38 × 106 m s −1

5. (a) 4 × 10−16 J (b) 2·96 × 107 m s −1 (c) 1·88 × 1016

6. (a) 1·25 × 1016 (b) 7·26 × 107 m s −1

7. (a) (i) 1·6 × 10−16 J (iii) 3·51 × 1015 m s −2 (iv) 5·34 × 10−9 s (v) 6·42 × 10−9 s (b) (i) Same since Q and V same (ii) Longer since acceleration is smaller

8. (a) 4·0 × 10−15 J (b) 9·37 × 107 m s −1 (c) 3·12 × 1016 (d) Heat and X-rays are produced

9. (a) Electron accelerated towards positive plate (b) Proton accelerated towards negative plate but less curved than that of electron (c) Neutron straight through.

10. (a) Negative (b) Positive (c) Positive (d) Negative

11. A = alternating electric fields; B = fixed-target; C = alternating electric fields; D = spiral of increasing radius; E = constant magnetic field; F = perpendicular; G = increases; H = physical size; I = relativistic effects; J = fixed-target; K = circular path of fixed radius; L = can be varied; M = alternating magnetic fields; N = increased; O = relativistic effects; P = the same; Q = opposite; R = colliding beam.

31 Section 3: Nuclear reactions

Fission and fusion

2. (i) ( a) 3 (b) 4 (ii) ( a) 30 (b) 34 (iii) ( a) 47 (b) 62 (iv) (a) 54 (b) 77 (v) (a) 94 (b) 145 (vi) (a) 103 (b) 154

3. A is or α B is C i s or β D is 4. α then β then α 5. A = 2 × 106 Bq

6. (a) 2·93 × 10−11 J (b) 1·81 × 10−11 J (c) 1·46 × 10−11 J (d) 2·57 × 10−11 J

7. (a) 3·209 × 10−29 kg (b) 2·89 × 10−12 J (d) 8·65 × 1018

8. (b) mass number 136, atomic number 52 (c) 1·62 × 10−28 kg (d) 1·46 × 10−11 J

32