P3 week 9 - Relativity and Nuclear Fission
Transcript of P3 week 9 - Relativity and Nuclear Fission
-
7/29/2019 P3 week 9 - Relativity and Nuclear Fission
1/18
Specialrelativity
Specialrela*vitypostulate1:
Thelawsofphysicsholdtrueforallframesofreference.Specialrela*vitypostulate2:
Thespeedoflightisaconstantforallframesofreference.
c
u
-
7/29/2019 P3 week 9 - Relativity and Nuclear Fission
2/18
Specialrelativity:Length
Contraction Objectstravellingclosetothespeedoflightseemtocontractinthedirec*onofmo*on
x
y
z
x'
y'
z'
L = L01
v2
c2
-
7/29/2019 P3 week 9 - Relativity and Nuclear Fission
3/18
Specialrelativity:Time
Dilation Timeisnotanabsolutequan*ty.Itisrela*ve Forobjectsmovingclosetothespeedoflight*meseemstorunslower
t=t0
1v2
c2
x
y
z
x'
y'
z'
-
7/29/2019 P3 week 9 - Relativity and Nuclear Fission
4/18
Thetwinparadox
Ifyouhadatwinandwhenyouwereboth20youboardedonaspaceshiptravellingat95%thespeedoflightwhilethey
stayedhereonEarthwhileyoutravelledfor25years(as
measuredbyyourclock)andcamebackwhenyouwere45,
howoldwouldyourtwinbe?
t=t0
1
v
2
c2
-
7/29/2019 P3 week 9 - Relativity and Nuclear Fission
5/18
Relativisticmass
Rest(orinvariant)mass=invariantquan*ty,sameinallreferenceframes
Rela*vis*cmass=dependentonthevelocityoftheobserver Theincreaseineffec*vemasswithspeedisgivenby
Rela*vis*cmassisatermusedwhenspeakingaboutthetotalenergyofasystem.
mr=
m0
1v2
c2
-
7/29/2019 P3 week 9 - Relativity and Nuclear Fission
6/18
Massandenergy
TheenergyE(inJoules)producedbyachangeofmassm(inkg)isgivenby
Wherec=speedoflight=3108m/s InnuclearphysicstheeVismorecommonlyusedastheunitofenergy:1eV=1.610-19J
1MeV=1.610-13J
E=mrc2
-
7/29/2019 P3 week 9 - Relativity and Nuclear Fission
7/18
Example
When1kgofwaterabsorbs4.2103Jofenergytoproducea
temperaturechangeof1K.Whatistheincreaseinthemassofthe
water?
-
7/29/2019 P3 week 9 - Relativity and Nuclear Fission
8/18
Example
Ifthemassdecreasemforthedecayof1atomofradiumis
8.6x10-30kg,howmuchenergyisreleased?
88
226Ra
2
4He+
86
222Rn
-
7/29/2019 P3 week 9 - Relativity and Nuclear Fission
9/18
Uni?iedatomicmass
Energycanalsobeexpressedintermsofmass Theunifiedatomicmassunit(u)isdefinedas1/12ththemassofthecarbonatom
Howmassiveis1u? 1u=1.6610-27kg 1u=931MeV
6
12C
-
7/29/2019 P3 week 9 - Relativity and Nuclear Fission
10/18
BindingEnergy
Theprotonsandneutronsinthenucleusofanatomarecallednucleons
Theworkofenergyneededtotakethenucleonsapartiscalledthebindingenergyof
thenucleus Itistheenergyassociatedwiththestrongnuclearforce
Themassdefect(ormassdifference)ofanucleusisdefinedasthedifferencebetweenthemassoftheseparatednucleonsandthe
combinedmassofthenucleus
Thebindingenergyistheenergyequivalentofthemassdifference(E=mc2)
-
7/29/2019 P3 week 9 - Relativity and Nuclear Fission
11/18
NuclearForcesandBinding
Energy Thesearetheforceskeepingatomicnucleitogether Theyarealwaysarac*ve Theyhaveaveryshortrange(oftheorderof2-3femto-meters(x10-15))
Anucleuswithanucleonnumber(massnumber)(N+Z)andaproton(atomicnumber)ZhasZprotonsandNneutrons
BindingenergyofatomBindingenergy=massofNneutrons+massofZprotonsmassofnucleus
atlessthan0.5fmthenuclearforceisrepulsivesothenucleonsdonottouch
Z
N+ZX
Z
N+ZX
-
7/29/2019 P3 week 9 - Relativity and Nuclear Fission
12/18
Example
AHeliumnucleushas4nucleons,2protonsand2neutrons.The
massofaprotonis1.0073uandthemassofaneutronis1.0087
u.IfthemassoftheHeliumnucleusis4.0015u,whatis
a)thebindingenergyofthenucleusinMeV?
b)thebindingenergypernucleoninMeV?
(1u=931MeV)
-
7/29/2019 P3 week 9 - Relativity and Nuclear Fission
13/18
Bindingenergycurve
Fusion
Fission
-
7/29/2019 P3 week 9 - Relativity and Nuclear Fission
14/18
Energyofdisintegration
Consideraradioac*vedecayprocessby-par2cleemission
atomicmasses:
Before:211.99127u 83me
Aer:(207.98201u 81me)+(4.002604u 2m
e)
Massloss:(totalmassbefore)(totalmassaer)=(211.99127u 83m
e)
(207.98201u 81m
e+4.002604u 2
me)=0.006656u =6.2MeV
83
212Bi
2
4He+
81
208Tl +Q
83
212Bi = 211.99127u
2
4He = 4.002604u 81
208Tl = 207.98201u
-
7/29/2019 P3 week 9 - Relativity and Nuclear Fission
15/18
Energyofdisintegration
Consideraradioac*vedecayprocessby-par2cleemission
atomicmasses:
Before:89.90730u -38me
Aer:(89.90670u 39me)+m
e
Massloss:(totalmassbefore)(totalmassaer)=(89.90730u 38m
e)
(89.90670u 39m
e+m
e)=0.00060u =
0.56MeV
38
90Sr
1
0e+
39
90Y+ v+Q
38
90Sr = 89.90730u
1
0e = 0.00055u =m
e 39
90Y = 89.90670u
-
7/29/2019 P3 week 9 - Relativity and Nuclear Fission
16/18
Energyofdisintegration
Consideraradioac*vedecayprocessby+-par2cleemission
atomicmasses:
Before:29.97832u -15me
Aer:(29.97376u 14me)+m
e
Massloss:(totalmassbefore)(totalmassaer)=(29.97832u 15m
e)
(29.97376u 13m
e)=0.00456u
20.00055u =0.00346u =3.22MeV
15
30P
+1
0e+
14
30Si++Q
15
30P = 29.97832u
+1
0e = 0.00055u =m
e 14
30Si = 29.97376u
-
7/29/2019 P3 week 9 - Relativity and Nuclear Fission
17/18
Nuclear?ission
Fissionhappenswhenaheavyatomicnucleussplitsintotwolighternuclei
Thenucleusisdeeplydividedintotwolargefissionfragmentsofroughlyequalmass
Themassdecrease(andhencetheenergyreleased,Q)isappreciable
Otherneutronsareemiedintheprocess(calledfissionneutrons)
92
235U+
0
1n
56
144Ba+
36
90Kr + 2
0
1n+Q
Chainreac2on:fissionneutronsproducefurtherfission
-
7/29/2019 P3 week 9 - Relativity and Nuclear Fission
18/18
ToDo
Readchapter30[p.614-626NuclearEnergy]