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


2/18

Specialrelativity:Length

Contraction Objectstravellingclosetothespeedoflightseemtocontractinthedirec*onofmo*on

x

y

z

x'

y'

z'

L = L01

v2

c2


3/18

Specialrelativity:Time

Dilation Timeisnotanabsolutequan*ty.Itisrela*ve Forobjectsmovingclosetothespeedoflight*meseemstorunslower

t=t0

1v2

c2

x

y

z

x'

y'

z'


4/18

Thetwinparadox

Ifyouhadatwinandwhenyouwereboth20youboardedonaspaceshiptravellingat95%thespeedoflightwhilethey

stayedhereonEarthwhileyoutravelledfor25years(as

measuredbyyourclock)andcamebackwhenyouwere45,

howoldwouldyourtwinbe?

t=t0

1

v

2

c2


5/18

Relativisticmass

Rest(orinvariant)mass=invariantquan*ty,sameinallreferenceframes

Rela*vis*cmass=dependentonthevelocityoftheobserver Theincreaseineffec*vemasswithspeedisgivenby

Rela*vis*cmassisatermusedwhenspeakingaboutthetotalenergyofasystem.

mr=

m0

1v2

c2


6/18

Massandenergy

TheenergyE(inJoules)producedbyachangeofmassm(inkg)isgivenby

Wherec=speedoflight=3108m/s InnuclearphysicstheeVismorecommonlyusedastheunitofenergy:1eV=1.610-19J

1MeV=1.610-13J

E=mrc2


7/18

Example

When1kgofwaterabsorbs4.2103Jofenergytoproducea

temperaturechangeof1K.Whatistheincreaseinthemassofthe

water?


8/18

Example

Ifthemassdecreasemforthedecayof1atomofradiumis

8.6x10-30kg,howmuchenergyisreleased?

88

226Ra

2

4He+

86

222Rn


9/18

Uni?iedatomicmass

Energycanalsobeexpressedintermsofmass Theunifiedatomicmassunit(u)isdefinedas1/12ththemassofthecarbonatom

Howmassiveis1u? 1u=1.6610-27kg 1u=931MeV

6

12C


10/18

BindingEnergy

Theprotonsandneutronsinthenucleusofanatomarecallednucleons

Theworkofenergyneededtotakethenucleonsapartiscalledthebindingenergyof

thenucleus Itistheenergyassociatedwiththestrongnuclearforce

Themassdefect(ormassdifference)ofanucleusisdefinedasthedifferencebetweenthemassoftheseparatednucleonsandthe

combinedmassofthenucleus

Thebindingenergyistheenergyequivalentofthemassdifference(E=mc2)


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


12/18

Example

AHeliumnucleushas4nucleons,2protonsand2neutrons.The

massofaprotonis1.0073uandthemassofaneutronis1.0087

u.IfthemassoftheHeliumnucleusis4.0015u,whatis

a)thebindingenergyofthenucleusinMeV?

b)thebindingenergypernucleoninMeV?

(1u=931MeV)


13/18

Bindingenergycurve

Fusion

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


15/18


Consideraradioac*vedecayprocessby-par2cleemission

atomicmasses:

Before:89.90730u -38me

Aer:(89.90670u 39me)+m

e


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


16/18


Consideraradioac*vedecayprocessby+-par2cleemission

atomicmasses:

Before:29.97832u -15me

Aer:(29.97376u 14me)+m

e


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


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


18/18

ToDo

Readchapter30[p.614-626NuclearEnergy]

p3 week 9 - relativity and nuclear fission

Documents