CHEM 312 Lecture 7 Fission Readings Modern Nuclear

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 7 -1

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 à 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 238 U undergoes fission spontaneously § half life of round 1016 y § Several other spontaneous fission isotopes found à Z > 90 § Partial fission half lives from nanoseconds to 2 E 17 years 7 -2

• 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 § follows 1/v law at low energies, sharp resonances at high energies 7 -3

Energetics Calculations • Why does 235 U undergo neutron induced fission for thermal energies? § Where does energy come from? • Generalized energy equation § AZ + n A+1 Z + E • For 235 U § E=(40. 914+8. 071)-42. 441 § E=6. 544 Me. V • For 238 U § E=(47. 304+8. 071)-50. 569 § E=4. 806 Me. V • For 233 U § E=(36. 913+8. 071)-38. 141 § E=6. 843 Me. V • Fission requires around 5 -6 Me. V 7 -4

Fission Process • Usually asymmetric mass split § MH/ML 1. 4 for uranium and plutonium § due to shell effects, magic numbers à 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, 235 U and 239 Pu § position of light peak increases • 2 peak areas for U and Pu thermal neutron induced fission • Influence of neutron energy observed 235 U fission yield 7 -5

• • • 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 7 -6

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. ” à two highly charged, deformed fragments in contact Large Coulomb repulsion accelerates fragments to 90% final kinetic energy within 10 -20 s 7 -7

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 § Cumulative yield: yield of an isobar à 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/c 2. htm 7 -8

Fission Process: Delayed Neutrons • Particles form more spherical shapes § Converting potential energy to emission of “prompt” neutrons § Gamma emission after neutrons § Then decay à 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 à 137 -139 I and 87 -90 Br as examples 7 -9

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 à Around 5 Me. V à neutron emission occurs 7 -10

Delayed Neutrons in Reactors • Control of fission § 0. 1 msec for neutron from fission to react à Need to have tight control à 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 235 U à 0. 26 % for 233 U and 0. 21 % for 239 Pu • Fission product poisons influence reactors § 135 Xe capture cross section 3 E 6 barns 7 -11

Nuclear reactors and Fission • Probable neutron energy from fission is 0. 7 Me. V § Average energy 2 Me. V § Fast reactors à High Z reflector § Thermal reactors need to slow neutrons à Water, D 2 O, graphite * Low Z and low cross section • Power proportional to number of available neutrons § Should be kept constant under changing conditions à Control elements and burnable poisons § k=1 (multiplication factor) à Ratio of fissions from one generation to next * k>1 at startup 7 -12

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 UO 2 crystal § 95 % of energy into stopping power à Remainder into lattice defects * Radiation induced creep § High local temperature from fission à 3300 K in 10 nm diameter 7 -13

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 by Coulomb barrier § Treat fission as barrier penetration àBarrier 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 Me. V 7 -14

Energetics • 200 Hg give 165 Me. V for Coulomb energy between fragments and 139 Me. V 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 7 -15

Half lives generally decrease rapidly with increasing Z 7 -16

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 238 U § Assume symmetric § 238 U 119 Pd + Q à Z=46, A=119 * Vc=462*1. 440/(1. 8(1191/3)2)=175 Me. V * Q=47. 3087 -(2*-71. 6203) = 190. 54 Me. V § asymmetric fission § 238 U 91 Br + 147 La + Q à Z=35, A=91 à Z=57, A=147 * Vc=(35)(57)*1. 44/(1. 8*(911/3+1471/3))=164 Me. V * Q=47. 3087 -(-61. 5083+-66. 8484) = 175. 66 Me. V Realistic case needs to consider shell effects § Fission would favor symmetric distribution without shell • • 7 -17

• • 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 a particles § Can also result from decay Fission Isomers 7 -18

Fission Isomers: Doublehumped fission barrier • At lower mass numbers, second barrier is ratedetermining, 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 7 -19

Proton induced fission • Energetics impact fragment distribution • excitation energy of fissioning system increases § Influence of ground state shell structure of fragments would decrease § Fission mass distributions shows increase in symmetric fission 7 -20

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 7 -21

Questions • Compare energy values for the symmetric and asymmetric fission of 242 Am. • 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 242 Am and 241 Am. Which isotope is likely to fission from an additional neutron. 7 -22

Pop Quiz • Provide calculations showing why 239 Pu can be fissioned by thermal neutron but not 240 Pu. • Compare the Q value and Coulomb energy (Vc) from the fission of 239 Pu resulting in 138 Ba and 101 Sr. Is this energetically favored? • Provide comments on blog • Bring to class on 17 October 7 -23