NE 301 - Introduction to Nuclear ScienceSpring 2012

Classroom Session 4:

•Radioactive Decay Types•Radioactive Decay and Growth•Isotopes and Decay Diagrams•Nuclear Reactions

• Energy of nuclear reactions• Neutron Cross Sections• Activation Calculations

2

Reminder

Load TurningPoint Reset slides Load List

The Energy Released (or consumed), Q

Change in BE:

Or since BE is related to mass defect

Change in M:

A + B C + D + E

( )C D A BQ BE BE BE BE BE

( )A B C DQ M M M M M

Preferred!because we have table B.1.

Remember: The Equation Has to Be

BALANCED!

Please remember…

BALANCE!

Before starting to work

5

Main Radioactive Decay Modes (Table 5.1 -page 89-Shultis)

Decay Type Description Emission

Gamma () Decay of excited nucleus

Gamma photon

alpha ()Alpha particle is emitted

Alpha particle

negatron (-) np++e-+ Electron and anti-neutrino

positron (β+) p+n+e++ Positron and neutrino

Electron Capture (EC)

Orbital e- absorbed: p++e-n +

Neutrino

proton (p) Proton ejected Proton

neutron (n) Neutron ejected Neutron

Internal Conversion (IC)

Electron (K-Shell) ejected*

Electron

Spontaneous Fission

(sf)

Fission fragments

*A AZ ZP P

1A AZ ZP D

42

A AZ ZP D

1A AZ ZP D

*1

A AZ ZP e D

*A AZ ZP P e

1 2 nAZ P D D x

6

7

Kinetic Energy of Radioactive Decay Products

Parent nucleus is at rest (Eth~ 0.025 eV~17 oC)

Conservation of Linear Momentum and Kinetic Energy requires products to travel in opposite directions (2 product).

m1v1=m2v2

Q=½ m1v12

+ ½ m2v22

What is the energy of emitted particle? (it is what we measure)

v1

m2

v2

m1

m1

m2

Original atom that will split in 2 pieces

8

Kinematics of radioactive decay…

2 21 1 2 2 1 1 2 2

2 21

1

2 22 21 2 2

1

2 22 22 2

2 2 2 2 21

22 2 2

1

2

1 1m v =m v Q= m v m v

2 2m v

v = replacing...m

m v1 1m ( ) m v

2 m 2

m v1 1 1m v and replacing m v by KE

2 m 2 2

m solving for KE

m

Q

Q

Q KE KE

KE Q

1 21

1 2 1 2

similarly: m m

KE Qm m m m

Notice 2:1

9

10

Main Radioactive Decay Modes (Table 5.1 -page 89-Shultis)

Decay Type Description Emission

Gamma () Decay of excited nucleus

Gamma photon

alpha ()Alpha particle is emitted

Alpha particle

negatron (-) np++e-+ Electron and anti-neutrino

positron (β+) p+n+e++ Positron and neutrino

Electron Capture (EC)

Orbital e- absorbed: p++e-n +

Neutrino

proton (p) Proton ejected Proton

neutron (n) Neutron ejected Neutron

Internal Conversion (IC)

Electron (K-Shell) ejected*

Electron

Spontaneous Fission

(sf)

Fission fragments

*A AZ ZP P

1A AZ ZP D

42

A AZ ZP D

1A AZ ZP D

*1

A AZ ZP e D

*A AZ ZP P e

1 2 nAZ P D D x

11

Beta Decay

Remember:’s DO NOT have

exactly defined energies

3 body interactionsMax energy =

neutrino took zero energy away…

What is this energy?Page 554

Page 98-Shultis

-, + produce three products:

Cannot say energy of Neutrinos by Fermi (1933)We only can say maximum energy of

13

Similarly for ’s

14

Kinetic Energy of De-excitation Decay

Details of the decays are needed to predict the correct spectrum.

Radioactive Decay Diagrams (e.g. book)

Write all 3 rxn shown

NiNi 6028

*6028

In principle gamma () photons would have Q of the reaction, but…

Q=2.50 MeV

16

Radioactive Decay Diagrams…In figure 5.6 Write all the reactions indicated in the

diagram.

If initially we have 100 g of 64Cu, how much Zn and Ni will we have after all Cu has decayed?

17

Branching Decay Example

1ln 20.0546

12.7h

h

?

?

?

?

EC

EC

1/ 2( )

1/ 2( )

1/ 2( )

1/ 2( )

?

?

?

?

EC

EC

T

T

T

T

1/2 T1/2 i

: is the frequency fraction or

TT

i T i i

i

f f

f

18

Branching Decay Example

-1ln 20.0546 h

12.7

1

1

1

1

0.005 0.0546 0.000273

0.431 0.0546 0.023533

0.174 0.0546 0.009500

0.390 0.0546 0.021294

EC

EC

h

h

h

h

1

0.000273 0.023533 0.009500 0.021294

0.0546

EC EC

h

19

On to

Binary Nuclear Reactions

Binary = 2 reactants (many times 2 products too)

Most important type of nuclear reactionMost elements produced by binary rxns. in stars

Nomenclature:

20

x X Y y Light nuclide usually projectile

Heavy nuclide usually target

Heavy Product

Light Product

21

Binary Reactions

(,p) First reaction reported by Rutherford:

Nitrogen in air bombarded by alphas producing protons

(,n) In 1932, the neutron was discovered (Chadwick).

Rxn. still used in some neutron generators today

24He 7

14N 817O1

1H or

714N(, p) 8

17O

24He4

9Be 612C0

1n or

49Be(,n) 6

12C

y)YX(x, or yYXx

22

Example Binary Reactions, cont.

(,n) Photo-nuclear rxns: Highly energetic gamma rays

can knock neutrons out of the nucleus.

(n,p) Fast neutrons react with oxygen in the water in a

reactor core producing radioactive 16N.

12H 1

1H01n or

12H(,n)1

1H

01n 8

16O 716N1

1p or

816O(n, p) 7

16C

or

12H(, p)0

1n

Mechanisms of Nuclear Reactions

Direct Interactions Projectiles w/

KE>40MeV have de Broglie wavelengths ~ size of a nucleon in target nucleus

Usually interact with individual nucleons

Near surface of nucleus (peripheral reactions)

Compound Nucleus Projectiles w/ KE ~

MeV have de Broglie wavelengths ~ size of the whole target nucleus

Usually interact with whole nucleus

Forms compound, highly excited nucleus

Products have no “memory” of the reactants.

23

( )*x X x X Y y

Reaction Nomenclature:

Transfer Reactions (,d) (d,n)

Scattering Reactions (x,x) elastic (x,x’) inelastic

Knockout Reactions (n,2n) (n,3n) (n,np)

Capture (n,)

Photo-Nuclear (,n)

24

Direct Reactions 1-2 nucleons transfer between projectile and target

projectile and target remain the same (it is a collision)

Direct Reaction: Original projectile emerges and is accompanied by other nucleons (i.e. spallation: SNS)

Projectile is absorbed by target nucleus (usually leaving it excited)

Strong gamma kicks nucleon from the target nucleus

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For Binary Reactions: x +X Y + yx is a projectile with KE (Ex). X is a target stationary nucleus EX=0

simplification

y Cosy

0, RealyE

26

y Cosy

0, RealyE

A 5.5 MeV particle is incident on Li causing 7Li(,n)10B. What is the KE of neutron scattered 30o?

A 5.5 MeV particle is incident on Li causing 7Li(,n)10B. What is the KE of neutron scattered 30o?

27

0, RealyE

y Cosy

1. 0 MeV2. 0.31 MeV3. 1.31 MeV4. 2.31 MeV5. 3.31 MeV6. 5.5 MeV

7Li(alpha,n)10B

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FIRST BALANCE THE EQUATION!!!

Endothermic Rxn

Neutron Energy = 1.31MeV

What would be the neutron energy if incident alpha particle is 1MeV instead?

Can’t happen…

Solution exists only if 0, RealyE

Potential “” Factors Q<0 Heavy projectiles (mY-mx<0) Large scattering angles Cos <0

Big enough Ex can guarantee Physical meaning: Threshold

Energy

0, RealyE

Argument of root >0