Nuclear Physics 2024 PDF

Nuclear Physics PH2106. Nicholas Devaney Learning Outcomes A short history of Nuclear Physics 1896 Henri Becquerel discovers Radioactivity by chance ! He found that uranium salts caused a photographic plate to be darkened and decided the Uranium must be emitting some radiation A short history...

Nuclear Physics PH2106. Nicholas Devaney Learning Outcomes A short history of Nuclear Physics 1896 Henri Becquerel discovers Radioactivity by chance ! He found that uranium salts caused a photographic plate to be darkened and decided the Uranium must be emitting some radiation A short history of Nuclear Physics 1898 Marie Curie discovers Polonium and Radium Had to process a ton of pitchblende to obtain 1/10 gram of radium chloride (1902) Nobel prize for Physics 1903 Nobel prize for Chemistry 1911 Using magnetic fields, it was found that there are three types of radioactivity (positive, negative and neutral = alpha, beta and gamma). A short history of Nuclear Physics Rutherford carried out the experiment shown here in 1899 The uranium ionizes the gas between the plates A and B. He placed varying thicknesses of Aluminium above the uranium and measured the current. Determined there were two types of radiation – alpha and beta “rays” In 1902 he succeeded in bending a beam of alpha particles in crossed electric and magnetic fields, proving it was a particle Nobel prize 1908 Rutherford’s gold foil experiment (1909) Also known as the Geiger-Marsden experiment Alpha particles cause flashes in zinc sulphide screen Scattered alpha particles detected at very large angles Rutherford model of mass concentrated in tiny nucleus with ‘orbiting’ electrons  Discovery of the neutron (1932) Rutherford had proposed the existence of a neutral particle to keep protons together in nuclei Chadwick bombarded a Beryllium target with alpha particles and allowed the resulting radiation to fall on Paraffin wax, which is rich in protons Determined that the unknown radiation must be neutral particles of similar mass to the proton Nobel prize 1935 Discovery of Fission From 1929 Otto Hahn, Fritz Strassmann and Leise Meitner were bombarding elements with neutrons and observing the results In 1938 they found they had produced Barium – much lighter than Uranium ! Explanation was that the Uranium nucleus had split into pieces – nuclear fission The sum of the masses is less than the original mass – nuclear energy  The Chicago pile, an experiment led by First controlled Enrico Fermi was the first controlled nuclear fission experiment. nuclear fission (1942) 45,000 graphite blocks (the moderator) 5.4 tonnes of Uranium metal 1945… The Manhattan project , led by Robert Oppenheimer, was set up to develop nuclear weapons during World War II The main effort was to produce enough uranium-235 and Plutonoum-239 Trinity test July 16 1945 August 6th 1945 Hiroshima August 9th Nagasaki About 225,000 casualties Isotopes Isotopes are atoms which: A. Have the same number of neutrons but different numbers of protons ? B. Have the same number of protons but different numbers of neutrons ? C. The same number of protons but different numbers of electrons ? Definitions… Protons and neutrons are both nucleons Number of neutrons plus protons is called the Mass number, or nucleon number Number of protons = Atomic number Definitions… Atomic mass unit (u) is defined as 1/12 the mass of the neutral Carbon-12 molecule Approximately equal to the mass of one nucleon (proton or neutron) 1u = 1.66×10&'( kg Convert to energy : 𝐸 = 𝑚𝑐 ' 𝑚𝑐 ' = 1.66×10&'( × 3×10. ' 1.49×10&12 𝐽 = 931.5 𝑀𝑒𝑉 Mass of neutral light nucleotides Nuclear binding energy Because of the strong nuclear force, the nucleons in a stable nucleus are held tightly together, therefore, energy is required to separate a stable nucleus into its constituent protons and neutrons. This energy is called binding energy If the sum of the individual masses of the separated protons and neutrons is greater by Dm than the mass of the stable nucleus. This mass difference is called the mass defect. The binding energy of a nucleus can be determined from the mass defect according to Einstein’s theory of special relativity: DE = Dmc2 1 u « 931.5 MeV/c 2 Binding energy = = 28.3 MeV Dm = 4.0330 u - 4.0026 u = 0.0304 u Nuclear binding energy Consider a neutral atom 98𝑀. If it is split into protons and neutrons, the energy required is given by: 𝐸: = 𝑍𝑚< + 𝑁𝑚? − 98𝑀 𝑐 ' Where 𝑚< is the mass of a neutral Hydrogen atom and 𝑚? is the neutron mass, and 𝑁 = 𝐴 − 𝑍 is the number of neutrons. Nuclear binding energy per nucleon An important measure of how tightly a nucleus is bound is the binding energy per nucleon. It is plotted below vs. A (=N+Z) Example: Nickel The strong nuclear force Keeps the neutrons and protons together despite electrical repulsion of the protons Short-range – only acts over nuclear dimensions (10-15m) Nucleons only interact with nearby nucleons Binding of pairs of protons or neutrons with opposite spins, or pairs of pairs, is particularly strong. Note: there is also a Weak nuclear force responsible for beta decay  The four forces https://csun.edu/science/csp/foss/e&m/four-forces.html The four forces Gravitational force – Gravitons (postulated) Weak force -- 𝑊 C , 𝑊 & , 𝑍 particles Electromagnetic force – photons Strong force – Gluons (postulated)  Segrè plot A plot of neutron number (N) against atomic number (Z) for all stable nuclides. For Z < 30, N=Z. For larger nuclei need more neutrons to stabilise All nuclei with Z>82 (Lead) are unstable Beta decay In some nuclides for which the neutron to proton ratio is too high for stability, a neutron can convert to a proton (which stays in the nucleus) an electron (ejected) and an antineutrino 𝑛 → p + 𝛽 & + 𝜈IK So in beta decay N decreases by 1, Z increases by 1 and A stays the same Radioactive decay series This Segrè chart shows the sequential decay from U-238 to lighter and smaller isotopes until finally reaching Pb-206. Nuclear reactions Like chemical reactions, nuclear reactions are balanced e.g. L'𝐻𝑒 + 1L(𝑁 → 1(.𝑂 + 1'𝐻 There is an additional conservation law: conservation of total number of nucleons (neutrons and protons) Like chemical reactions, heat is absorbed or emitted when initial particles A and B interact to produce final particles C and D, the reaction energy Q is found from neutral atomic masses MA,B,C,D 𝑄 = (𝑀9 +𝑀: − 𝑀Q − 𝑀R )𝑐 ' Nuclear reactions 𝑄 = (𝑀9 +𝑀: − 𝑀Q − 𝑀R )𝑐 ' If Q>0, the total mass decreases and the total kinetic energy increases “exothermic” If Q < 0, the mass increases and the kinetic energy decreases “endothermic” In the endothermic case the initial kinetic energy has to be at least as big as 𝑄 for the reaction to happen. Nuclear reaction example When a lithium-7 nucleus is bombarded by a proton, two alpha particles are produced. Find the reaction energy. 1 1𝐻 + (T𝐿𝑖 → L'𝐻𝑒 + L'𝐻𝑒 𝑄 = (𝑀9 +𝑀: − 𝑀Q − 𝑀R )𝑐 ' Nuclear reaction example When a lithium-7 nucleus is bombarded by a proton, two alpha particles are produced. Find the reaction energy. 1 ( L L 1 𝐻 + T 𝐿𝑖 → ' 𝐻𝑒 + '𝐻𝑒 𝑄 = (𝑀9 +𝑀: − 𝑀Q − 𝑀R )𝑐 ' A: 11𝐻 1.007825 u C: LT𝐻𝑒 4.002603 u B: (T𝐿𝑖 7.016005 u D: L'𝐻𝑒 4.002603 u 8.023830 u 8.005206 u Endothermic or Exothermic ? Nuclear reaction example When a lithium-7 nucleus is bombarded by a proton, two alpha particles are produced. Find the reaction energy. 1 ( L L 1 𝐻 + T 𝐿𝑖 → ' 𝐻𝑒 + '𝐻𝑒 𝑄 = (𝑀9 +𝑀: − 𝑀Q − 𝑀R )𝑐 ' The mass decreases by 0.018624 u, so Exothermic 𝑀𝑒𝑉 𝑄 = 0.018624 𝑢 931.5 = +17.35 𝑀𝑒𝑉 𝑢 Nuclear fission I A large nucleus splits or is split into smaller nucleotides of comparable mass Induced fission is a result of neutron absorption and fission fragments are usually not equal Fission fragments always have too many neutrons to be stable and undergo a series of beta- decays: the “droplet model” of fission Nuclear fission II Nuclear fission reactions require enough material to sustain the cascade. This effect is called a “chain reaction,” and the amount of material is called “the critical mass.” Nuclear chain reaction:  Nuclear reactors Controlled fission requires thermal control (with circulating water) and “moderation” of neutrons (with graphite or water). Moderation means slowing down the neutrons. This is required to keep the fission chain reaction going. The reaction can be controlled by using control rods of material which absorbs neutrons. Cadmium and boron are strong neutron absorbers and are the most common materials used in control rods. Nuclear fusion Lighter isotopes are added together to make a heavier one (nuclear fusion). During fusion and fission the binding energy per nucleon after the reaction is greater than before The energy released is immense. This is the reaction that powers the Sun and stars The chain is conversion of four protons into one alpha particle (4He) with resulting energy. Proton-proton chain (Sun’s interior) X2 Net effect: convert four protons into one 𝛼 particle, two positrons, two electron neutrinos, and two 𝛾. Also 2.044 (=4 x 0.511) MeV from annihilation of positrons with electrons. There are enough protons in the sun to power fusion for about 10 billion years (age is 4.54 billion years) Fusion for energy ? For nuclei to fuse, they need to come together closer than 2×10&1] m. Must overcome electrical repulsion of the protons before the Strong nuclear force can take over Two protons at 2×10&1] m, potential energy about 0.7 MeV. This kinetic energy is needed for the nuclei to fuse. At temperature T, the average translational kinetic energy of a gas molecule T is given by 𝐸 = 𝑘𝑇, where k is Boltzmann’s constant. ' This implies a temperature of 3×10` 𝐾. Temperature at center of Sun ‘only’ 1.5×10( 𝐾, so fusion occurs with low probability, and the sun lasts longer. National Ignition Facility 192 high-power lasers directed onto a deuterium+tritium fuel capsule The capsule implodes raising the density to 100s x density of lead, and temperature to 100s x million degrees In 2021 NIF produced 70% of the energy of the laser ITER – Fusion Project Multi-national project to demonstrate fusion power generation Reaction temperature 100×10b K Plasma of Deuterium+Tritium heated by electric current, confined in double-steel chamber Superconducting magnets keep the plasma from touching the walls by magnetic confinement Demonstrate better than break-even fusion by 2035… Types of particles Fermions – spin ½, 3/2, 5/2… Bosons – spin 0,1,2 Fermions obey the Pauli exclusion principle Bosons do not Two types of Fermion Leptons (do not take part in strong interactions) Quarks (take part in all interactions) Leptons Ordinary matter  Quarks Nucleons made up of u and d quarks u quarks charge = 2/3 e D quarks charge = -1/3 e Any particle made of of two or more quarks is called a Hadron  Mesons = quark + antiquark Particle with an odd number of quarks = a Baryon