Nuclear Reactions & Applications Nuclear Reactions • Nuclear Reactions: x+X!y+Y or X(x,y)Y Q = (Initial Mass) c2 – (Final Mass) c2 = (Mxc2+MXc2) – (Myc2+MYc2) Example: α + 14N ! p + 17O or 14N(α,p)17O Q = (Initial Mass) c2 – (Final Mass) c2 = (Mαc2+M14Oc2) – (Mpc2+M17Oc2) [Can be generalized to any (low energy) reactions: X1+X2 ! Y1+Y2+Y3+…] (Spontaneous) Fission Some heavy isotopes can fission spontaneously into two so-called “fission fragments” (+ possibly some neutrons…) Ex: 256Fm (t1/2=2.6 h) 254Cf (t =60.5 days) 1/2 The fission fragments are statistically distributed over a large range of medium-mass nuclei and are usually radioactive (and β-decay back to stability) ! How fast depends of the half-lives of the isotopes formed on the way ! Induced Fission Because the neutron has no charge, it can penetrate the nucleus (no Coulomb barrier) ! Neutron used as a Probe. Example: 1938-39: Induced fission of 238U ! large release of energy (~200 MeV) ! new neutrons are emitted !!! ! CHAIN REACTION POSSIBLE ? Leo Szilard Thermal Neutron Mechanism • Fission fragments are highly unstable because they are so neutron rich. • Prompt neutrons are emitted simultaneously with the fissioning process. Even after prompt neutrons are released, the fission fragments undergo beta decay, releasing more energy. • Most of the ~200 MeV released in fission goes to the kinetic energy of the fission products, but the neutrons, beta particles, neutrinos, and gamma rays typically carry away 30–40 MeV of the kinetic energy. U-235 Fission Cross Section Faster Neutrons Chain Reaction • More than one neutron (on average) is emitted after every fission: possibility of triggering a chain reaction. • Neutrons emitted are “fast neutrons”, need to be slowed down (“slow/thermal neutrons”). [Fission cross sections increases by 1/v] • Chain Reactions: – Slightly more than one neutron emitted per reaction ! chain reaction critical – Less than one neutron ! subcritical – More than one neutron ! supercritical Applications of induced fission Controlled: Nuclear Power Plant Waste: long-lived fission fragments (ex: 90Sr, 137Cs…) Uncontrolled: Atomic Bomb (A-bomb) Hiroshima: Energy released 1014 Joules = 20 kilotons of TNT Nasty stuff (after blast): fission fragments ! Reading: “The making of the Atomic Bomb” (Richard Rhodes) Nuclear Reactor Core: Moderator [hydrogen in water, beryllium, carbon in graphite]: ! slows down the neutrons to “thermal” energies Control rods [Boron for example] ! absorbs the neutron excess, control the criticality of the reactor Reflector [hydrogen in water] ! allows backscattering of the neutrons back in the cells. Power Plants Example: Fusion Fusion releases more energy per nucleon than fission. However, this process doesn’t occur spontaneously. One needs to ignite the reaction, then the energy produced has to self-sustain the fusion process. That’s what is happening in the Sun: 4 1H ! (several steps) !4He, Q=26.7 MeV (then: 3 4He ! 12C, etc…) Applications to induced fusion Controlled: Nuclear Fusion Power Plant (projects: tokamaks, laser…) New initiative: ITER project Problem: Ignition ! Uncontrolled: Hydrogen Bomb (H-bomb) requires an A-bomb to ignite fusion !!! Enhanced yield: Hundreds of kilotons ! Tens of Megatons ! (Hiroshima, 20 kt) Reading: “Dark Sun” (Richard Rhodes) (Ivy) Mike – Oct Device: 60 tons, Yield: 10.4 MT st 31 , 1952 Castle Bravo Expected Yield: 4-8 MT Measured Yield: 15MT !!! First lithium-deuteride “dry” bomb: 40%: 6Li ! d, t, n… 60%: 7Li + n ! 6Li + 2n (Oops!!!) A fusion reactor ? Inertial Confinement Application: Oil & Mining Neutron sources: PuBe or AmBe sources Many more applications • Archeology: 14C (t1/2 ~ 5730 years) • Medicine: X-rays, radioactive tracers (ex: …) + imagery, radiotherapy 99m Tc, • Engineering: γ-radiography of material, neutron activation, thickness control… • Other applications: Smoke detector, Sterilization, … Carbon-14 Dating 14C is a radioactive isotope of carbon with a half-life of t1/2=5730y. It is produced in our atmosphere by the bombardment of 14N by neutrons (produced by cosmic rays). 1. Write the reaction that produces 14C. 14C can be absorbed by a living organism the same way than the stable carbon isotope 12C. The equilibrium ratio R0 = N(14C)/N(12C) in the atmosphere has been measured to be 1.20x10-12. When an organism dies, it ceases absorbing carbon (both 12C and radioactive 14C) and therefore the ratio R(t) changes over time as 14C nuclei decay. Application: a bone suspected to have originated during the period of the roman emperors was found in Great Britain. The N(14C)/N(12C) ratio was determined to be 1.10x10-12. 2. Write the radioactive decay law for the 14C nuclei. Express the decay law using R(t) and R0. 3. How old is the bone according to the 14C dating method? Is the bone old enough to have Roman origins? 99mTc – T1/2=6.01h Metastasis Radiotherapy Radiotherapy delivered internally Radiotherapy delivered externally CAT scan Computer Assisted Tomography