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CHEM 312 Lecture 7: Fission

- Readings: Modern Nuclear Chemistry, Chapter 11; Nuclear and Radiochemistry, Chapter 3
- General Overview of Fission
- Energetics
- The Probability of Fission
- Fission Product Distributions
- Total Kinetic Energy Release
- Fission Product Mass Distributions
- Fission Product Charge Distributions
- Fission in Reactors
- Delayed neutron
- Proton induced fission

Nuclear Fission

- Fission discovered by Otto Hahn and Fritz Strassman, Lisa Meitner in 1938
- Demonstrated neutron irradiation of uranium resulted in products like Ba and La
- Chemical separation of fission products
- For induced fission, odd N
- Addition of neutron to form even N
- Pairing energy
- In 1940 G. N. Flerov reported that 238U undergoes fission spontaneously
- half life of round 1016 y
- Several other spontaneous fission isotopes found
- Z > 90
- Partial fission half lives from nanoseconds to 2E17 years

Fission

- Can occur when enough energy is supplied by bombarding particle for Coulomb barrier to be surmounted
- Fast neutron
- Proton
- Spontaneous fission occurs by tunneling through barrier
- Thermal neutron induces fission from pairing of unpaired neutron, energy gain
- Nuclides with odd number of neutrons fissioned by thermal neutrons with large cross sections
- follows1/v law at low energies, sharp resonances at high energies

Energetics Calculations

- Why does 235U undergo neutron induced fission for thermal energies?
- Where does energy come from?
- Generalized energy equation
- AZ + n A+1Z + E
- For 235U
- E=(40.914+8.071)-42.441
- E=6.544 MeV
- For 238U
- E=(47.304+8.071)-50.569
- E=4.806 MeV
- For 233U
- E=(36.913+8.071)-38.141
- E=6.843 MeV
- Fission requires around 5-6 MeV

Usually asymmetric mass split

MH/ML1.4 for uranium and plutonium

due to shell effects, magic numbers

Heavy fragment peak near A=132, Z=50, N=82

Symmetric fission is suppressed by at least two orders of magnitude relative to asymmetric fission

Occurs in nuclear reactions

Competes with evaporation of nucleons in region of high atomic numbers

Location of heavy peak in fission remains constant for 233,235U and 239Pu

position of light peak increases

2 peak areas for U and Pu thermal neutron induced fission

Influence of neutron energy observed

Fission Process235U fission yield

Fission Process

- Fission yield curve varies with fissile isotope
- Heavier isotopes begin to demonstrate symmetric fission
- Both fission products at Z=50 for Fm
- As mass of fissioning system increases
- Location of heavy peak in fission remains constant
- position of light peak increases

Fission Process

- Nucleus absorbs energy
- Excites and deforms
- Configuration “transition state” or “saddle point”
- Nuclear Coulomb energy decreases during deformation
- Nuclear surface energy increases
- Saddle point key condition
- rate of change of Coulomb energy is equal to rate of change of nuclear surface energy
- Induces instability that drives break up of nucleus
- If nucleus deforms beyond this point it is committed to fission
- Neck between fragments disappears
- Nucleus divides into two fragments at “scission point.”
- two highly charged, deformed fragments in contact
- Large Coulomb repulsion accelerates fragments to 90% final kinetic energy within 10-20 s

Fission

- Primary fission products always on neutron-excess side of stability
- high-Z elements that undergo fission have much larger neutron-proton ratios than stable nuclides in fission product region
- primary product decays by series of successive - processes to its stable isobar
- Yields can be determined
- Independent yield: specific for a nuclide
- Cumulativeyield: yield of an isobar
- Beta decay to valley of stability
- Data for independent and cumulative yields can be found or calculated
- For reactors
- Emission of several neutrons per fission crucial for maintaining chain reaction
- “Delayed neutron” emissions important in control of nuclear reactors

Comparison of cumulative and independent yields for A=141

http://www-nds.iaea.org/sgnucdat/c2.htm

Fission Process: Delayed Neutrons

- Particles form more spherical shapes
- Converting potential energy to emission of “prompt” neutrons
- Gamma emission after neutrons
- Then decay
- Occasionally one of these decays populates a high lying excited state of a daughter that is unstable with respect to neutron emission
- “delayed” neutrons
- 0.75 % of total neutrons from fission
- 137-139I and 87-90Br as examples

Delayed Neutrons

- Fission fragments are neutron rich
- More neutron rich, more energetic decay
- In some cases available energy high enough for leaving residual nucleus in such a highly excited state
- Around 5 MeV
- neutron emission occurs

Delayed Neutrons in Reactors

- Control of fission
- 0.1 msec for neutron from fission to react
- Need to have tight control
- 0.1 % increase per generation
- 1.001^100, 10 % increase in 10 msec
- Delayed neutrons useful in control
- Longer than 0.1 msec
- 0.65 % of neutrons delayed from 235U
- 0.26 % for 233U and 0.21 % for 239Pu
- Fission product poisons influence reactors
- 135Xe capture cross section 3E6 barns

Nuclear reactors and Fission

- Probable neutron energy from fission is 0.7 MeV
- Average energy 2 MeV
- Fast reactors
- High Z reflector
- Thermal reactors need to slow neutrons
- Water, D2O, graphite
- Low Z and low cross section
- Power proportional to number of available neutrons
- Should be kept constant under changing conditions
- Control elements and burnable poisons
- k=1 (multiplication factor)
- Ratio of fissions from one generation to next
- k>1 at startup

Fission Process and Damage

- Neutron spatial distribution is along direction of motion of fragments
- Energy release in fission is primarily in form of kinetic energies
- Energy is “mass-energy” released in fission due to increased stability of fission fragments
- Recoil length about 10 microns, diameter of 6 nm
- About size of UO2 crystal
- 95 % of energy into stopping power
- Remainder into lattice defects
- Radiation induced creep
- High local temperature from fission
- 3300 K in 10 nm diameter

Fission Energetics

- Any nucleus of A> 100 into two nuclei of approximately equal size is exoergic.
- Why fission at A>230
- Separation of a heavy nucleus into two positively charged fragments is hindered byCoulomb barrier
- Treat fission as barrier penetration
- Barrier height is difference between following
- Coulomb energy between two fragments when they are just touching
- energy released in fission process
- Near uranium both these quantities have values close to 200 MeV

Energetics

- 200Hg give 165 MeV for Coulomb energy between fragments and 139 MeV for energy release
- Lower fission barriers for U when compared to Hg
- Coulomb barrier height increases more slowly with increasing nuclear size compared to fission decay energy
- Spontaneous fission is observed only among very heaviest elements
- Half lives generally decrease rapidly with increasing Z

Energetics

- Generalized Coulomb barrier equation
- Compare with Q value for fission
- Determination of total kinetic energy
- Equation deviates at heavy actinides (Md, Fm)
- Consider fission of 238U
- Assume symmetric
- 238U119Pd + 119Pd + Q
- Z=46, A=119
- Vc=462*1.440/(1.8(1191/3)2)=175 MeV
- Q=47.3087-(2*-71.6203) = 190.54 MeV
- asymmetric fission
- 238U91Br + 147La + Q
- Z=35, A=91
- Z=57, A=147
- Vc=(35)(57)*1.44/(1.8*(911/3+1471/3))=164 MeV
- Q=47.3087-(-61.5083+-66.8484) = 175.66 MeV
- Realistic case needs to consider shell effects
- Fission would favor symmetric distribution without shell

Fission Isomers

- Some isomeric states in heavy nuclei decay by spontaneous fission with very short half lives
- Nano- to microseconds
- De-excite by fission process rather than photon emission
- Fissioning isomers are states in these second potential wells
- Also called shape isomers
- Exists because nuclear shape different from that of ground state
- Proton distribution results in nucleus unstable to fission
- Around 30 fission isomers are known
- from U to Bk
- Can be induced by neutrons, protons, deuterons, and aparticles
- Can also result from decay

Fission Isomers: Double-humped fission barrier

- At lower mass numbers, second barrier is rate-determining, whereas at larger A, inner barrier is rate determining
- Symmetric shapes are most stable at two potential minima and first saddle, but some asymmetry lowers second saddle

Proton induced fission

- Energetics impact fragment distribution
- excitation energy of fissioningsystem increases
- Influence of ground state shell structure of fragments would decrease
- Fission mass distributions shows increase in symmetric fission

Topic Review

- Mechanisms of fission
- What occurs in the nucleus during fission
- Understand the types of fission
- Particle induced
- Spontaneous
- Energetics of fission
- Q value and coulomb barrier
- The Probability of Fission
- Cumulative and specific yields
- Fission Product Distributions
- Total Kinetic Energy Release
- Fission Product Mass Distributions

Questions

- Compare energy values for the symmetric and asymmetric fission of 242Am.
- What is the difference between prompt and delayed neutrons in fission.
- What is the difference between induced and spontaneous fission.
- What influences fission product distribution?
- Compare the Coulomb barrier and Q values for the fission of Pb, Th, Pu, and Cm.
- Describe what occurs in the nucleus during fission.
- Compare the energy from the addition of a neutron to 242Am and 241Am. Which isotope is likely to fission from an additional neutron.

Pop Quiz

- Provide calculations showing why 239Pu can be fissioned by thermal neutron but not 240Pu.
- Compare the Q value and Coulomb energy (Vc) from the fission of 239Pu resulting in 138Ba and 101Sr. Is this energetically favored?
- Provide comments on blog
- Bring to class on 17 October

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