Presentation on theme: "++ Y = S + B I 3 = Q + ½Y –– K+K+ K0K0 K0K0 K–K– 00 00."— Presentation transcript:
++ Y = S + B I 3 = Q + ½Y –– K+K+ K0K0 K0K0 K–K– 00 00
The Nucleus Atoms consist of a positively charged nucleus plus electrons Nuclear charge is Ze, where Z is an integer called the atomic number This determines what chemical element it is +Ze -e-e -e-e -e-e -e-e The mass/potential energy (E 0 =mc 2 ) of a neutral atom has three components: The mass of the nucleus The mass of the electrons – there are Z of these The binding energy of the electrons Binding energy is tiny, so Tables of isotopes give the mass of the neutral atom in u
The Mass of an atom Not all neutral atoms of the same element have the same mass Atoms come in different isotopes with different masses All isotopes have masses that are approximately integer multiples of the same common unit The atomic mass unit (u) is defined as 1/12 of 12 C atom The integer closest to M/u is called A, the mass number 11 Li: u 118 Sn: u Avogadro’s number The ratio of u to g is called Avogadro’s number Useful for lots of problems
The size of the nucleus Can be measured in various ways My favorite: replace an electron by the 200 times heavier muon Wave function is 200 times smaller The wave function responds to the finite nuclear size Radius goes crudely as A 1/3 Volume roughly proportional to number of nucleons Isotopes are described by telling their charge Z, their atomic mass number A, and the name of the chemical symbol The chemical symbol X tells you Z, so normally skipped Sometimes an isotope has a bit of extra energy – we call it an isomer Denoted by putting a * on it Almost always very unstable Naming isotopes +Ze
The composition of the nucleus All normal nuclei have only two types of particles in them: The proton has charge +e There are Z of these The neutron has charge 0 There are N of these Electrons are not found in the nucleus The mass of an atom is protons + neutrons + electrons + binding To a crude approximation, this is just the number of protons + neutrons This is why the mass is almost an integer +e+e+e+e 0 0 # ParticleMassQ Z Proton u+e N Neutron u0 Electron u-e What is Z, N, A, and the approximate mass of 235 U?
Radioactivity Many nuclei decay over time This is a quantum mechanical process – you can’t predict when it will happen If you have a lot of atoms, the rate at which they decay will be proportional to the number of atoms The radioactivity destroys the atoms Integrate to see how number changes with time N is number of atoms N 0 is initial number of atoms is the decay rate Also, multiply by R is the rate at which atoms are decaying R 0 is the initial rate Half-life, t 1/2 is the time it takes for half the atoms to decay Let’s find a formula for it
Sample problem 134 Cs has a half-life of 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 = 10 4 s -1 ?
Particles and anti-particles Several particles are important for understanding nuclear processes Protons, neutrons, and electrons have already been discussed The photon is a particle of light The neutrino is a massless (or nearly massless) neutral particle ParticleMass (MeV)Sym. Proton up + Neutron un 0 Electron ue - Photon u Neutrino u anti-Elec ue + anti-Neut u p+p+ n0n0 e-e- e+e+ Anti-Particles For every particle, there is an anti-particle Same mass, opposite charge Some particles (the photon) are their own anti-particles For nuclear physics, the important ones are the anti-electron and anti-neutrino
Neutron decay and anti-particles Particle processes are a lot like equations You can turn them around and they still work You 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) p+p+ n0n0 e-e- The neutron (in isolation) is an unstable particle Decays to proton + electron + anti-neutrino This occurs in – decay ++ p+p+ e-e- ++ n0n0 Turn the reaction around Put the neutrino on the other side This occurs in electron capture p+p+ e-e- + n0n0 + Put the electron on the other side This occurs in + decay p+p+ n0n0 + + e+e+
Calculating Energetics in a decay Nuclear decay is when an isolated nucleus spontaneously breaks apart Typically (not always), there is one Parent nucleus and one Daughter nucleus Also, typically, some other particles too PD + ? We want to know how much energy is released The potential energy of each component is just mc 2 The difference between these values is Q – the energy available Unfortunately, we aren’t given the nuclear masses, just the atomic This energy generally appears as kinetic energy, mostly of the lighter products on the right (the ? particles) This formula is just a bridge to the formulas we really want
Nuclear Decay Processes There are many types of decay processes, we will focus on only the most common Our goal is to figure out how to calculate, for those we consider: The daughter isotope (Z,A) The energy Q produced Whether the process actually occurs Processes can occur if Q > 0 We won’t worry about How slowly it goes (some virtually never occur) (higher Q helps) Which are more likely than others (higher Q helps) – decay Electron capture + decay Spontaneous fission decay decay PD + ?
– decay – is another name for the electron and + for the positron A neutron inside a nucleus can decay to a proton Example: 3 H 3 He p+p+ n0n0 n0n0 p+p+ e-e- The daughter nucleus: Total number of nucleons unchanged Charge increases by 1 (Z,A) (Z+1,A) The change in energy (Q): p+p+ n0n0 e-e- ++
p+p+ p+p+ p+p+ n0n0 n0n0 n0n0 Electron capture A proton in the nucleus captures one of the electrons in the atom Example: 7 Be 7 Li The daughter nucleus: Total number of nucleons unchanged Charge decreases by 1 (Z,A) (Z-1,A) The change in energy (Q): p+p+ e-e- + n0n0 + e-e- p+p+ n0n0
A proton in the nucleus decays to a neutron Example: 11 C 11 Be The daughter nucleus: Total number of nucleons unchanged Charge decreases by 1 (Z,A) (Z-1,A) The change in energy (Q): + decay p+p+ p+p+ p+p+ p+p+ p+p+ n0n0 n0n0 n0n0 n0n0 n0n0 p+p+ n0n0 p+p+ n0n0 + + e+e+ e+e+
Sample problem What would be the resulting isotope and the Q-value for each of the following decays of 40 K? (a) - decay(b) electron capture(c) + decay Z el.A mass (u) 18 Ar K Ca - decay: (Z,A) (Z+1,A) Daughter is 40 Ca
Sample problem What would be the resulting isotope and the Q-value for each of the following decays of 40 K? (a) - decay(b) electron capture(c) + decay Z el.A mass (u) 18 Ar K Ca Electron capture: (Z,A) (Z-1,A) Daughter is 40 Ar + decay: (Z,A) (Z-1,A) Daughter is 40 Ar
A large nucleus has a lot of electrostatic repulsion It would like to separate, but strong forces hold it together More on this later It is possible, but rare for it to break apart into two (or more) pieces Commonly, neutrons are emitted as well. Spontaneous Fission A quantum tunneling process Very rare when large chunks are involved No naturally occurring elements We need a small, very stable chunk to make this work better The particle is such a chunk P D1D1 D2D2 n0n0 n0n0
The particle is the nucleus of Helium – it is very stable Two protons and two neutrons Because it is light, it has a good chance of tunneling out Decay p+p+ p+p+ n0n0 n0n0 PD p+p+ p+p+ n0n0 n0n0 The daughter nucleus: Nucleons decrease by four Charge decreases by two (Z,A) (Z–2,A–4 ) The change in energy (Q): m + 2m e is just the mass of a helium atom
Sometimes, nuclei have internal energy Like an atom in an excited state Like an atom, the energy comes out in the form of a photon Decay P The daughter nucleus: No change in nucleons (Z,A)* (Z,A ) The change in energy (Q): D How did we get an excited nucleus in the first place? Usually a byproduct of a previous nuclear decay To us, this just looks like it came from the Cobalt
Summary Radiation Hazards All 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 Decay Z AFormula for Q +2+4(M P – M D – M 4He )c 2 – +1 0(M P – M D )c 2 e.c.–1 0(M P – M D )c 2 + –1 0(M P – M D )c 2 – 2 m e c 2 0 0(M P – M D )c 2