Presentation on theme: "Advanced Topics Nuclear Physics ElementaryParticles General Relativity"— Presentation transcript:
1 Advanced Topics Nuclear Physics ElementaryParticles General Relativity Y = S + BK0K+–0+0I3 = Q + ½YK–K0ElementaryParticlesGeneral Relativity
2 Tables of isotopes give the mass of the neutral atom in u Nuclear PhysicsThe NucleusAtoms consist of a positively charged nucleus plus electronsNuclear charge is Ze, where Z is an integer called the atomic numberThis determines what chemical element it is-eThe mass/potential energy (E0=mc2) of a neutral atom has three components:The mass of the nucleusThe mass of the electrons – there are Z of theseThe binding energy of the electronsBinding energy is tiny, so-e+Ze-e-eTables of isotopes give the mass of the neutral atom in u
3 The Mass of an atom Avogadro’s number Not all neutral atoms of the same element have the same massAtoms come in different isotopes with different massesAll isotopes have masses that are approximately integer multiples of the same common unitThe atomic mass unit (u) is defined as 1/12 of 12C atomThe integer closest to M/u is called A, the mass number11Li: u118Sn: uAvogadro’s numberThe ratio of u to g is called Avogadro’s numberUseful for lots of problems
4 Naming isotopes The size of the nucleus Isotopes are described by telling their charge Z, their atomic mass number A, and the name of the chemical symbolThe chemical symbol X tells you Z, so normally skippedSometimes an isotope has a bit of extra energy – we call it an isomerDenoted by putting a * on itAlmost always very unstableThe size of the nucleusCan be measured in various waysMy favorite: replace an electron by the 200 times heavier muonWave function is 200 times smallerThe wave function responds to the finite nuclear sizeRadius goes crudely as A1/3Volume roughly proportional to number of nucleons+Ze
5 What is Z, N, A, and the approximate mass of 235U? The composition of the nucleusAll normal nuclei have only two types of particles in them:The proton has charge +eThere are Z of theseThe neutron has charge 0There are N of theseElectrons are not found in the nucleus# Particle Mass QZ Proton u +eN Neutron u 0Electron u -e+e+eThe mass of an atom is protons + neutrons + electrons + bindingTo a crude approximation, this is just the number of protons + neutronsThis is why the mass is almost an integerWhat is Z, N, A, and the approximate mass of 235U?
6 Radioactivity Many nuclei decay over time This is a quantum mechanical process – you can’t predict when it will happenIf you have a lot of atoms, the rate at which they decay will be proportional to the number of atomsThe radioactivity destroys the atomsIntegrate to see how number changes with timeN is number of atomsN0 is initial number of atoms is the decay rateAlso, multiply by R is the rate at which atoms are decayingR0 is the initial rateHalf-life, t1/2 is the time it takes for half the atoms to decayLet’s find a formula for it
7 Sample problem 134Cs has a half-life of 2.065 y. What is the decay rate ?If we start with g, what is the initial decay rate?How long must we wait until the decay rate is less than Ci = 104 s-1?
8 Particles and anti-particles Several particles are important for understanding nuclear processesProtons, neutrons, and electrons have already been discussedThe photon is a particle of lightThe neutrino is a massless (or nearly massless) neutral particleParticle Mass (MeV) Sym.Proton u p+Neutron u n0Electron u e-Photon u Neutrino u anti-Elec u e+anti-Neut u p+n0e-e+Anti-ParticlesFor every particle, there is an anti-particleSame mass, opposite chargeSome particles (the photon) are their own anti-particlesFor nuclear physics, the important ones are the anti-electron and anti-neutrino
9 Neutron decay and anti-particles Particle processes are a lot like equationsYou can turn them around and they still workYou can move particles to the other side by “subtracting them”This means replacing them with anti-particles(However, you have to make sure energy works)The neutron (in isolation) is an unstable particleDecays to proton + electron + anti-neutrinoThis occurs in – decay++n0p+e-Turn the reaction aroundPut the neutrino on the other sideThis occurs in electron capture++n0p+e-++p+n0e-Put the electron on the other sideThis occurs in + decay++p+n0e+
10 This formula is just a bridge to the formulas we really want Calculating Energetics in a decayNuclear decay is when an isolated nucleus spontaneously breaks apartTypically (not always), there is one Parent nucleus and one Daughter nucleusAlso, typically, some other particles tooPD+?We want to know how much energy is releasedThe potential energy of each component is just mc2The difference between these values is Q – the energy availableUnfortunately, we aren’t given the nuclear masses, just the atomicThis formula is just a bridge to the formulas we really wantThis energy generally appears as kinetic energy, mostly of the lighter products on the right (the ? particles)
11 Nuclear Decay Processes There are many types of decay processes, we will focus on only the most commonOur goal is to figure out how to calculate, for those we consider:The daughter isotope (Z,A)The energy Q producedWhether the process actually occursProcesses can occur if Q > 0We won’t worry aboutHow slowly it goes (some virtually never occur) (higher Q helps)Which are more likely than others (higher Q helps)PD+?– decayElectron capture+ decaySpontaneous fission decay decay
12 ++ – decayn0p+e-– is another name for the electron and + for the positronA neutron inside a nucleus can decay to a protonExample: 3H 3Hep+n0p+e-The daughter nucleus:Total number of nucleons unchangedCharge increases by 1(Z,A) (Z+1,A)The change in energy (Q):
13 Electron capture + + p+ e- n0 A proton in the nucleus captures one of the electrons in the atomExample: 7Be 7Lip+n0e-The daughter nucleus:Total number of nucleons unchangedCharge decreases by 1(Z,A) (Z-1,A)n0p+The change in energy (Q):
14 + decay + + p+ n0 e+ A proton in the nucleus decays to a neutron Example: 11C 11BeThe daughter nucleus:Total number of nucleons unchangedCharge decreases by 1(Z,A) (Z-1,A)p+n0n0p+e+The change in energy (Q):
15 Sample problem Z el. A mass (u) 18 Ar 36 35.967547 37 36.966776 19 K20 CaSample problemWhat would be the resulting isotope and the Q-value for each of the following decays of 40K?(a) - decay (b) electron capture (c) + decay- decay: (Z,A) (Z+1,A)Daughter is 40Ca
16 Sample problem Z el. A mass (u) 18 Ar 36 35.967547 37 36.966776 19 K20 CaSample problemWhat would be the resulting isotope and the Q-value for each of the following decays of 40K?(a) - decay (b) electron capture (c) + decayElectron capture: (Z,A) (Z-1,A)Daughter is 40Ar+ decay: (Z,A) (Z-1,A)Daughter is 40Ar
17 Spontaneous FissionA large nucleus has a lot of electrostatic repulsionIt would like to separate, but strong forces hold it togetherMore on this laterIt is possible, but rare for it to break apart into two (or more) piecesCommonly, neutrons are emitted as well.PD2D1n0n0A quantum tunneling processVery rare when large chunks are involvedNo naturally occurring elementsWe need a small, very stable chunk to make this work betterThe particle is such a chunk
18 Decayp+n0The particle is the nucleus of Helium – it is very stableTwo protons and two neutronsBecause it is light, it has a good chance of tunneling outDPThe daughter nucleus:Nucleons decrease by fourCharge decreases by two(Z,A) (Z–2,A–4 )p+n0The change in energy (Q):m + 2me is just the mass of a helium atom
19 Decay Sometimes, nuclei have internal energy Like an atom in an excited stateLike an atom, the energy comes out in the form of a photonThe daughter nucleus:No change in nucleons(Z,A)* (Z,A )DPThe change in energy (Q):How did we get an excited nucleus in the first place?Usually a byproduct of a previous nuclear decayTo us, this just looks like it came from the Cobalt
20 Summary Radiation Hazards Decay Z A Formula for Q (MP – MD – M4He)c2– (MP – MD)c2e.c. –1 0 (MP – MD)c2+ –1 0 (MP – MD)c2 – 2 mec2 (MP – MD)c2Radiation HazardsAll of these processes (except electron capture) produce high-energy ionizing radiation that can be extremely damaging to you particles are easily stopped, by paper or dead skin, if they are outside your body radiation can penetrate more deeply, so they are more dangerous radiation is very penetrating, and hence is most dangerous
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