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8.6Massandenergy
Wehavealreadycomeacrossmass-energyequivalenceintheparticlephysics
unit.The‘restenergy’(E)isproportionaltothe‘restmass’(m):
𝐸 = 𝑚𝑐 % wherecisaconstant=speedoflightinavacuum= 3×10+ 𝑚𝑠 -. Forexample,whenanelectronandapositronannihilate,twoparticleswithmass
producetwomasslessphotons.Therestenergycanbecalculatedusingthe
energyequivalenceequation,above.Thisrestenergythenappearsastheenergy
ofthetwophotons(𝐸 = ℎ𝑓, 𝑤ℎ𝑒𝑟𝑒𝑓 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦𝑎𝑛𝑑ℎ𝑖𝑠𝑡ℎ𝑒𝑃𝑙𝑎𝑛𝑐𝑘𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡).
(1)!Therestmassofanelectron=9.11×10-C. 𝑘𝑔.Workouttherestenergyofan
electroni)injoules,ii)inMeV.(Remember1𝑒𝑉 ≡ 1.6×10-.H 𝐽)
(2)!Workoutthefrequencyofthephotonsproducedwhenanelectronand
positronannihilate.(Assumethattheirinitialkineticenergyiszero)
Whenthepotentialenergyofasystemisincreased,thereisanincreaseinthe
massofthesystem.Forexample,whenanobjectisliftedupintheEarth’s
gravitationalfield,thepotentialenergyofthesystem(theEarthandtheobject)
isincreased,andthereisanequivalentincreaseinthemassofthesystem.
Thesameistruefornucleonsinanatom.Whennucleonsarebroughttogether,
thepotentialenergy(duetothestrongnuclearforce+theelectrostaticforce)is
decreased.Thismeansthatthemassofthenucleusislessthanthemassofthe
separatenucleons.Thisiscalledthe‘massdefect’(Δ𝑚)andisequivalent(from
𝐸 = Δ𝑚𝑐 % )toanenergycalledthe‘bindingenergy’.
Letusconsideranexample.
Therestenergyofaproton=938.08MeV.Therestenergyofaneutron=
939.37MeV.Therestenergyofaheliumnucleus=3727.6MeV.
(3)!Giventhattheheliumnucleushastwoprotonsand2neutrons,workoutthe
restenergyoftheseparatenucleonsaddedtogether.Comparethiswiththerest
energyoftheheliumnucleus.
Youshouldfindthattherestenergyhasdecreased.Thedifferenceiscalledthe
bindingenergyoftheheliumnucleus.Inconstructingtheheliumnucleus,energy
mustbereleased.
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Nuclear,mass-energycalculationsofteninvolveinterchangingbetweenmass
andenergy!Considerthefollowing:
massofproton=1.00728u
massofneutron=1.00867u
.
whereuiscalledthe‘unifiedatomicmassunit’andis ofthemassofacarbon-12atom
.%
(atrest).
Amassof1uisequivalenttoanenergy=931.3MeV.
(4)!Krypton-92hasarestmassof91.8976u.Ithasaprotonnumber(atomic
number)=36.Workoutthemassdefect,inu,ofitsnucleus.Workoutthebinding
energy,inMeV,ofitsnucleus.
Bindingenergypernucleon
Themassofanucleondependsonthenucleusitispartof.Theimages,below
showtherelativemassesofnucleonsindifferentnuclei.Thesmallerthemass,
thelargerthebindingenergypernucleon.
Fe
U
r
H
Wecansee,from
thegraphicabove,
thattheprotonina
hydrogenhasthe
largestmass
(becauseitisnot
boundtoanother
nucleon).Anucleon
inanironnucleus
hasthesmallest
mass(becausethe
bindingenergyper
nucleonisthe
greatest).
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Inconstructinganynucleus,(binding)energyisreleasedandthemassofthe
nucleonsdecreases.
energy
Innuclearfission,alargenucleusissplitandthenucleonsinthenucleiofthe
productshaveasmallermass.Thisdecreaseinmassisaccompaniedbyarelease
ofenergy.
energy
Innuclearfusion,smallernucleiarefusedtogethertoformalargernucleus.The
massofthenucleonsdecreases.Thisisaccompaniedbyareleaseofenergy.
energy
(5)!Inafusionreactor,deuterium( %.𝐻)andtritium( C.𝐻)arefusedtogetherto
make L%𝐻𝑒andaneutron.Energyisreleasedasthekineticenergyoftheproducts.
Workoutthechangeinmass,andhencetheenergy
releasedinthisprocess.(massof %.𝐻=2.01410u,mass
of C.𝐻=3.01605u,massof L%𝐻𝑒=4.00260u,massof
neutron=1.00867u).
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