Chapter 1

Learning Objectives

• Historical R e c a p

• U nderstand the different length scales of nu c l e a r p h y s i c s

• K now the nomenclature for isotopes and nuclear reactions

• K now the different types of neutron nuclear c o l l i s i o n s a n d t h e i r relationship t o each other

• B a s i c p r i n c i p l e s o f n u c l e a r r e a c t o r

Learning Objectives

• N eutron Sources

• B asic Principles of Nuclear Reactor

• B indin g ener g y curve

• Liquid drop model

• F ission Reaction

• ODE Review

• R adioactive Decay

• D ecay Chains

• C hart of Nuclides

Historical Recap

• D r i s c o l l h a n d o u t

• N ew programs

– GNEP/AFCI

– G en-IV

– Nuclear Power 2010

W h y nuclear?

• P o w e r d e n s i t y

– 1000 MW electric

• 1 0 0 0 0 t ons o f coa l per D A Y ! !

• 20 tons of uranium per YEAR (of which only 1 ton is U - 235)

A typical pellet of uranium weighs about 7 grams (0.24ounces). It can generate as much energy as……

3.5 barrel s of oi l or…… 17,000 cubic feet of natural gas, or… .. 1,780 pounds of coal.

Why nuclear?

• Why still use coal

– C a p i t a l c o s t

– P olitics

What do you think is the biggest barrier to constructing the next U.S. nuclear power plant?

50%

40%

30%

20%

10%

0% Political Nuclear W aste Resistance to Disposal

Nuclear Ener gy Issues

Cost of Nuclear Power Plant Construction

Fear of Nuclear Accident

Other

– P u b l i c p e r c e p t i o n of n u c l e a r , n u c l e a r w a s t e r issue

- 2008 surve y of energy professionals

Image by MIT OpenCourseWare.

“ Eighty - t w o p e r c e n t o f A m e r i c a n s living i n close proximity to nuclear power plants f a v o r nuclear e n e r g y , a n d 7 1 percent a r e willing to see a new reactor built near them , a c c o r d i n g t o a new p u b l i c o p i n i o n survey of more than 1,100 adults

nationwide . ” – N E I , S eptember 2 0 0 7

B a s i c P r i n c i p l e s of N u c l e a r R e a c t o r

• S i m p l e d e v i c e

– F issioning fuel releases energy in the “core”

– H e a t is t r a n s p o r t e d a w a y by a c o o l a n t w h i c h couples the heat source to a Rankine steam cycle

– V ery similar to a coal plant, with the exception of the combustion p rocess

– M ain complication arises from the spent fuel, a mix of over 300 fission p roducts

Public domain image from wikipedia.

Main T urbine

Electric Generator

Main Condenser

• P o w e r p l a n t s w i l l

o f t e n

Circulating W ater Pump

discharge their circ ulating water directly back to the ocean

– Strict environmental pro t ec t i on regu l a t i ons

– Temperature increases by 5 - 1 0 F a r e n h e i t s

Image by MIT OpenCourseWare.

Electric

Main Generator T urbine

Main Condenser

Cooling T ower

Circulating W ater Pump

Image by MIT OpenCourseWare.

• If far from a water source, coo li ng towers are use d to transfer the heat to air.

– W a t e r v a p o r i s v i s i b l e a t t h e contact of the warm wet air inside the tower with the cool dry air outside

R e a c t o r s C o n cepts

• Fuel

– U ranium

– Plutonium

– Thorium

• M oderator (optional)

– L ight water

– H eavy water

– Graphite

– Be

• Coolant

– L ight water

– Heav y wate r

– S odium

– Molten salt

– H elium

– C O 2

– L ea d - B i smu t h

– …

M acroscop i c t o m i croscop i c wor l d

C utaway of PWR pressure vessel and I nternals.

Fission chain reaction

Public domain image from wikipedia. Public domain image from wikipedia.

Nomenclature -- Isotopes

A X s u ch as 12 C or

23 5 U

Z 6 9 2

Z is the atomic number

A is the atomic mass

N = A-Z is the number of neutrons N uclei with the same Z and dif f erent A are called isotopes.

E.g. 23 5 U

a nd

23 8

92

1 H a n d 2 H

a nd 3 H

Nuclear Stability

Image removed due to copyright restrictions.

• A s Z i n c r e a se s , the long range Coulomb repulsion between protons is balanced by the presence of a dditi ona l neu t rons t o provide additional short - range a t t r a c t i v e nuclear forces.

D i s t r i b u t i o n of Stable N u c l i d e s

Nuclear Collision Reactions

a + b c + d a(b, c)d

1 n 

23 5 U

 23 6 U  

0 92 92

23 5

92

( n ,  )

23 6

92

F u n d a m e n t a l L a w s

• C o n s e r v a t i o n o f n u c l e o n s

– T otal “A” remains the same

• Conservation of charge

– T otal “Z” remains the same

• C onservation of momentum

• C onservation of Ener gy

– E nergy, including rest mass, is conserved

Rest Mass

E 2 _

(pc) 2 = (mc 2 ) 2

Mass is a characteristic of the total ener gy and momentum of an object or a system of objects that is the same in all frames of reference.

m 0 = E/c 2

The invariant mass of the system is equal to the total system ener gy divided by c 2 .

This total ener gy in the center of momentum frame, is the minimum ener gy which the system may be observed to have.

Special Relativity Mass

m = m 0

A body ’ s mass increases when it is in motion with speed v relative to an observer at rest.

Q - value

Exothermic reaction produces ener gy Endothermic reaction requires ener gy

An exothermic reaction is defined with Q < 0 therefore it is important to understand the concept:

E = mc 2

Q = [( M a + M b ) _ ( M c + M d )] c 2

Q > 0 exothermic

Q < 0 endothermic

E a + E b

+ M a c 2

+ M b c 2 = E c + E d

+ M c c 2 + M d c 2

Examples of Q-value

Exothermic

Q = [ M

( 9 Be) + M ( 4 He ) _ M ( 12 C)

_ m n ]c 2

4 2 6

Q = [9.012182u + 4.002603u _

12.000000u

_ 1.008664u]931.5MeV/u

Q = 5.702MeV

9 Be + 4 He 12 C + 1 n

4 2 6 0

Examples of Q-value

Endothermic

Q = [ M ( 1 6 O) + m n

_ M ( 1 3 C)

_ M ( 4 He) ]c 2

Q = [15.994915u + 1.008664u _

_ 4.002603u]931.5MeV/u

13.003354u

Q = _ 2.215MeV

1 6 O + 1 n 13 C + 4 He

8 0 6 2

Examples of Q-value

1 6 O( n,p ) 16 N

8 7

Assumption

Q    m n  M  16 O   M  16 N   m p   c 2

8 7

Why is this incorrect?

1 n  1 6 O  1 6 N 

 0 e  1 p

This is approximately equivalent to

1 n  16 O  16 N  1 H

0 8 7 1

Q    m n  M  16 O   M  16 N   M  1 H    c 2

Most important Reactions

An Example

235 U + 1 n 129 I + 10 4 Y + 3 1 n

92 0 53 39 0

Nuclear fission (n, fission)

1 n  A X  A 1 X  A 2 X

 neutrons  200 Me V

0 Z Z 1 Z 2

Radiative Capture

An Example

238 U + 1 n ( 239 U) * 239 U + 0 

92 0 92 92 0

Radiative capture (n,  )

1 A A  1

0 Z Z

 * 

A  1  

Scattering

Examples

elastic 12 C + 1 n 12 C + 1 n

6 0 6 0

inelastic

(  Pu +  n  Pu)* +  n  Pu +   +  n

Scattering ( n, n ) or ( n, n' )

1 n 

A X 

1 n 

A X elastic scattering (n,n)

1 n 

A X 

1 n  

A X  * 

1 n 

A X  

inelastic scattering (n,n')

Beta decay

When the weak interaction converts a neutron into a proton and emits an electron and an anti-neutrino, Beta (minus) decay occurs. This happens when an atom has an excess of neutrons.

A X  0 e  A Y  _

 E nerg y

Z  1 Z  1 

_

13 7

55

13 7 Ba +

0 e + 

Positron Emission

Positron emission cannot occur in isolation unlike Beta deca y .

This happens because it requires ener gy (the mass of the neutron is greater than the mass of the proton).

Positron emission happens inside the nuclei when the absolute value of the binding ener gy of the mother nucleus is lower than that of the daughter nucleus.

A X + Ene r gy A Y + 0 e + 

Z Z-1 1

22 Na 22 Ne + 0 e + 

1 1 10 1

Capture of Electron

A X + 0 e + Ene r gy A Y + 

Z -1 Z-1

In cases where ß+ decay is allowed ener geticall y , it is accompanied by the electron capture process.

22 Na + 0 e 22 Ne + 

1 1 -1 10

If the ener gy dif ference between initial and final states is low (less than 2 m e c 2 ), then  decay is not ener getically possible and electron capture is the sole mode deca y .

Alpha Decay

Coulomb repulsion increases ~ Z 2

Alpha decay occures only in heavy atoms (A > 100 amu )

Alpha particle has small mass relative to parent nucleus and has very high binding ener gy

Nuclear binding force increases ~ A

A X  + A- 4 Y + Ene r gy

Z

238

92

Z-2

234 Th + a

Gamma decay

27

Co 60

5.26 a

60

28

Ni

Image by MIT OpenCourseWare.

• G amma decay is the emission of a gamma ray (photon) from a nucleus

• O c c u r s w h e n nucleus transitions f r o m a h i g h e r t o l o w e r e n e r g y s t a t e

• E nergy of photon(s) equal to the change in energy of nuclear states

• Nuclear structure does not change so parent and daughter are the same

Predicting type of decay

90

80



70

60

Line of Stability

50

40

 

30

20

10

0

0

10 20 30 40 50 60 70 80 90 100 1 10 120 130 140

Neutron (N)

Image by MIT OpenCourseWare.

Binding Ener gy

  ZM p + NM n - M X

The weights of these constituent masses exceeds the weight of the nucleus if we add the masses of Z protons and N neutrons that make up a nucleus.

The dif ference is the mass defect which is positive for all nuclides. Multiplying by c 2 yields the binding ener gy of the nucleus.

When the nucleus is formed, the loss in mass is due to the conversion of mass to binding energy . It is defined as the ener gy that is supplied to a nucleus to completely separate its nucleons.

A measure of nuclear stability is obtained when the binding ener gy is normalized to the number of nucleons.

Calculate mass defect and binding energy f or uran i um- 23 5

M a s s o f n e u t r o n 1 . 0 0 8 6 6 5 amu Mass of proton 1.007826 amu

M ass o f one a t om o f U- 235 235 . 043924 Binding energy = mass defect x c 2

• M a s s defect = 1 . 9 1 5 1 7 amu

• BE = 1 . 91517 amu x 931 .5 Me V / 1 amu

• BE = 1784 MeV

1 a m u =

1 . 66054 x 10 -27 kg =

931 . 5 M e V / c 2

B i n d i n g Energy C u r v e

• E xothermic reactions result in reaction products with higher binding energy

• T wo op ti ons

– Fission of heavy nuclides

– Fusion of light nuclides

First - O r d e r O D E - Review

• A p p e n d i x A of L e w i s + H andout

Radioactive D e c a y

• Le w i s , S e c t i o n 1 . 7

Decay c h a i n

(a)  B = 5 x  A ; t 1 = 5 x t 1

1 2 A 2 B

0.75

0.5

0.25

0

0 1

(b)  B =  A / 5; t 1 A = t 1 B / 5

2 3 4

t

(c)  B =  A ; t 1 A = t 1 B

2 2

1

0.75

0.5

0.25

0 0 1 2 3 4

t

1 2 2

0.75

0.5

0.25

0

0 1 2 3 4

t

Image by MIT OpenCourseWare.

Decay Chains

Definition of Decay Chain: The radioactive decay of dif ferent discrete radioactive decay products as a chained series of transformations.

Decay Chains

_ Thorium series or 4n

_ Neptunium series or 4n + 1

_ Uranium or Radium series 4n + 2

_ Actinium series or 4n + 3

C h a r t o f N uclides

Image by MIT OpenCourseWare.

Chart of Nuclides

• G r a y shaded square (stable n u c l i d e )

Symbol, mass number

Percent abundance Activation cross-section in

"bars" to two isomers Mass (C-12 scale)

Fission product, slow neutron fission of U-235

Pd 108

26.71

 (0.2 + 12)

107.9030

Image by MIT OpenCourseWare.

Fe 52

8 h

B 0.80, (263), 

 0.17, 380, (1.43)

E 2.38

• White or "color" square: ( Artificially Produced Radioactive Nuclide )

Symbol, mass number

Half life

Modes of decay , radiation, and ener gy in Me V . ( ) means radiation from short-lived daughter .

Disintegration ener gy in Me V .

Image by MIT OpenCourseWare.

C h a r t o f N uclides

• B lack rectangles across the top of square

– On gray-shaded square: R adioactive nuclide with long half life (Considered Stable)

Symbol

Ce 142

1 1.07

Percent abundance

Half life

5 x 10 15 yrs

 , 1.5

 1

141.9090

Modes of decay

Thermal neutron absorption cross-section

in barns

Mass

Image by MIT OpenCourseWare.

– On white square: Radioactive nuclide found in n a t u r e with r e l a t i v e l y s hort h a l f life

C h a r t o f N uclides

• S maller black rectan g le near to p

of s q uare

( Nuclide is a

member of a natural radioactive decay chain)

Po 218

Ra A

 6.00



3.05 m

218.0089

Symbol, mass number

Symbol Half life

Modes of decay and ener gies

Mass

Image by MIT OpenCourseWare.

• B lack triangle at bottom corner of square ( nuclide is

formed b y

fission of U-235 or Pu-239 )

Pd 108

26.71

 (0.2 + 12)

107.9030

Symbol, mass number

Percent abundance

Mass (C-12 scale)

Activation cross-section in "bars" to two isomers

Fission product, slow neutron fission of U-235

Image by MIT OpenCourseWare.

C h a r t o f N uclides

• V e r t i c a l l y divided s q uare

– T wo isomeric states, one stable

Symbol

Half life

Modes of decay radiation, and ener gies in Mev

14 d

IT 0.159

 0.161

e -

Sn 1 17

7.61

1 16.9031

Percent abundance

Mass

Radioactive upper isomer

Stable lower isomer

Image by MIT OpenCourseWare.

– T wo isomeric states, both radioactive

Symbol

Radioactive upper isomer

? 16d

  0.45

Pm 145

18y

 ,e -

 0.068, 0.073

E 0.14

Half life, ?

means uncertainty

Modes of decay radiation, and ener gies in Mev

Disintegration ener gy in Mev

Stable lower isomer

Image by MIT OpenCourseWare.

Neutron Sources

Definition of Spontaneous Fission

Spontaneous fission (SF) is a form of radioactive decay characteristic for very heavy isotopes. In practice, only ener getically feasible for atomic masses above 230 amu. It is theoretically possible for any atomic nucleus with mass >= 100 amu.

Radioisotopes for which spontaneous fission is a nonnegligible decay mode may be used as neutron sources notably Cf-252 (half-life 2.645 years, SF branch ratio 3.09%)

10 2

10 1

10 0

1

2

3

4

5

Neutron ener gy (MeV)

Measured neutron ener gy spectrum from the spontaneous fission of 252 Cf.

Image by MIT OpenCourseWare.

• A lpha Neutron Source

– Neutrons are produced when alpha particles impinge upon any of several low atomic weight isotopes

• beryllium, carbon and oxygen

• M ust have loosel y bound neutron

– Alpha emitters must be long-lived

• R adium, polonium, plutonium, americium

– T he low A material and alpha emitter are usually mixed in powdered form

– T ypical emission rates for alpha reaction neutron sources range from 1×10 6 to 1×10 8 neutrons per second.

– Th e s i ze an d cos t o f th ese neu t ron sources are a l so compara bl e to spontaneous fission sources.

– U sual combinations of materials are plutonium-beryllium (PuBe), americium - b e r y l l i u m ( A mB e ) , o r a m e r i c i u m - l i t h i u m (A m L i )

– R adium is not used as much now because of its high gamma emission rate

8

6

Stilbene

4

Emulsions

2

0

2

4

6

8

10

Neutron ener gy (MeV)

Measured ener gy spectra for neutrons from a 239 Pu/Be source containing 80g of the isotope.

Image by MIT OpenCourseWare.

• P hotoneutrons

– A photon that is absorbed by t he nucleus creates an excited state from which a neutron is emitted. There are two such sources:

– 9 Be + >1.7 Mev photon → 1 neutron + 2 4 He

– 2 H ( d e u t e r i u m ) + > 2 . 26 M e V p h o t o n → 1 neutron + 1 H

– T he resulting neutron energies ar e discrete if the photons are monoenerge ti c. R oughl y, one gamma ray i n 106 int erac t s. S o, the gamma ray source needs to be very large (as in a fission reactor) for these sources to be appreciable. The most common u s e is t h e d e u t e r i u m r e a c t i o n a s a s o u r c e o f n e u t r o n s f o r t h e startup of light-water reactors. The source of the photons would be fission products. (Note: Sufficient D 2 O exists in light water for t h i s s o u r c e t o b e e f f e c t i v e i n L W R s . )

• A c c e l e r a t e d c h a r g e d p a r t i c l e s

• F ission

• F us i on

• …

Fission

• C onsider the followin g exam p le of U-235 fission

• From binding energy curve, energy released is about

~200 MeV (235*(8.9 – 8 ))

– Most of the energy leaves in the form of kinetic energy of the fission products

– R e s t go e s to p a r t ic l e s emitted d u r i n g f i s s i o n

• A distinction must be made betw een energy produced and energy recuperated – Fission products are large ionized particles that travel a short distance, thus

e e n n e e r r g g y y is deposited l l o o c c a a l l l l y y

– The electrons released by beta decay of the fission products are also absorbed locally.

– T he gamma rays (photons) travel much greater distances and are sometimes a b sor b e d b y t h e reac t or s h i e l d .

– The neutrinos escape entirely

Image by MIT OpenCourseWare.

• For fission to occur, we must provide some energy to the

nucleus. A

p otential barrier exists that

p revents

spontaneous fission from happening very frequently.

• L iquid drop model: A water drop doesn’t separate in two s p o n t a n e o u s l y e ve n i f i t s e n e r g e t i c a l l y f a v o r a b l e . T h e superficial tension of the drop acts as a barrier that tries to keep the fragments from splitting.

Image by MIT OpenCourseWare.

• I n nuclear fission, the short nucl ear bonds of the nucleons keeps the nucleus together . Initially , the potential energy of the nucleus is equal to the binding energy of the nuc leons (no kinetic energy). To deform the nucleus, energy must be pr ovided in an effort to increase the average distance between the nucleons, thus increasing the potential energy of the nucleus . However , the strong nuclear forces are very short. Thus when the separation starts, the repulsive forces diminish and the potential ener gy diminishes as well. There is thus a threshold energy required (about 6 MeV) for fission

• Q uan t um mec h an i cs a l so exp lai ns h ow spon t aneous fi ss i on can happen, but with very-low probability, thru a tunnelling effect without any energy input.

• W hen a neutron interacts with a nuclide, it forms a compoun d nuc l eus. E nergy i s g i ven t o th e nuc l eus b y the binding energy of the incident neutron and its kinetic energy

– If the binding energy is sufficient to get above the fission threshold of the nuclide, than t he nuclide is fissile to thermal neutrons

– If it requires additional kinetic energy, than it is said to be fissile to f ast neutrons or f issionable

• F issile nuclides

– U -235: only naturally occurring fissile isotope

– P u- 239 : ra di at i ve capture o f U - 238

– U -233: radiative capture of Th-232

– Pu-241: radiative capture of Pu-240

Critical Energy

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Fission cross sections for fi ss i ona b l e nuc l e i