Advanced Topics Nuclear Physics ElementaryParticles General Relativity Y = S + B K0 K+ – 0 + 0 I3 = Q + ½Y K– K0 ElementaryParticles General Relativity

Tables of isotopes give the mass of the neutral atom in u Nuclear Physics 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 -e The mass/potential energy (E0=mc2) 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 -e +Ze -e -e Tables of isotopes give the mass of the neutral atom in u

The Mass of an atom Avogadro’s number 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 12C atom The integer closest to M/u is called A, the mass number 11Li: 11.0438 u 118Sn: 117.9016 u Avogadro’s number The ratio of u to g is called Avogadro’s number Useful for lots of problems

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 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 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 A1/3 Volume roughly proportional to number of nucleons +Ze

What is Z, N, A, and the approximate mass of 235U? 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 # Particle Mass Q Z Proton 1.007276 u +e N Neutron 1.008665 u 0 Electron 0.000549 u -e +e +e 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 What is Z, N, A, and the approximate mass of 235U?

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 N0 is initial number of atoms  is the decay rate Also, multiply by  R is the rate at which atoms are decaying R0 is the initial rate Half-life, t1/2 is the time it takes for half the atoms to decay Let’s find a formula for it

Sample problem 134Cs has a half-life of 2.065 y. What is the decay rate ? If we start with 1.000 g, what is the initial decay rate? How long must we wait until the decay rate is less than 1.000 Ci = 3.700  104 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 Particle Mass (MeV) Sym. Proton 1.007276 u p+ Neutron 1.008665 u n0 Electron 0.000549 u e- Photon 0.000000 u  Neutrino 0.000000 u  anti-Elec. 0.000549 u e+ anti-Neut. 0.000000 u  p+ n0 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) The neutron (in isolation) is an unstable particle Decays to proton + electron + anti-neutrino This occurs in – decay + + n0 p+ e-  Turn the reaction around Put the neutrino on the other side This occurs in electron capture + + n0 p+ e-  + + p+ n0 e-  Put the electron on the other side This occurs in + decay + + p+ n0  e+

This formula is just a bridge to the formulas we really want 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 P D + ? We want to know how much energy is released The potential energy of each component is just mc2 The difference between these values is Q – the energy available Unfortunately, we aren’t given the nuclear masses, just the atomic This formula is just a bridge to the formulas we really want This energy generally appears as kinetic energy, mostly of the lighter products on the right (the ? particles)

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) P D + ? – decay Electron capture + decay Spontaneous fission  decay  decay

+ +  – decay n0 p+ e-  – is another name for the electron and + for the positron A neutron inside a nucleus can decay to a proton Example: 3H  3He p+ n0 p+ e- The daughter nucleus: Total number of nucleons unchanged Charge increases by 1 (Z,A)  (Z+1,A)  The change in energy (Q):

Electron capture + + p+ e- n0  A proton in the nucleus captures one of the electrons in the atom Example: 7Be  7Li p+ n0 e- The daughter nucleus: Total number of nucleons unchanged Charge decreases by 1 (Z,A)  (Z-1,A) n0 p+  The change in energy (Q):

 + decay + + p+ n0  e+ A proton in the nucleus decays to a neutron Example: 11C  11Be The daughter nucleus: Total number of nucleons unchanged Charge decreases by 1 (Z,A)  (Z-1,A) p+ n0 n0 p+  e+ The change in energy (Q):

Sample problem Z el. A mass (u) 18 Ar 36 35.967547 37 36.966776 37 36.966776 38 37.965903 39 38.964314 40 39.962384 42 41.963049 19 K 39 38.963708 40 39.964000 41 40.961827 42 41.962404 43 42.960716 20 Ca 40 39.962591 41 40.962279 42 41.958618 43 42.858767 44 43.955481 46 45.953687 48 47.952534 Sample problem What 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

Sample problem Z el. A mass (u) 18 Ar 36 35.967547 37 36.966776 37 36.966776 38 37.965903 39 38.964314 40 39.962384 42 41.963049 19 K 39 38.963708 40 39.964000 41 40.961827 42 41.962404 43 42.960716 20 Ca 40 39.962591 41 40.962279 42 41.958618 43 42.858767 44 43.955481 46 45.953687 48 47.952534 Sample problem What would be the resulting isotope and the Q-value for each of the following decays of 40K? (a) - decay (b) electron capture (c) + decay Electron capture: (Z,A)  (Z-1,A) Daughter is 40Ar + decay: (Z,A)  (Z-1,A) Daughter is 40Ar

Spontaneous Fission 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. P D2 D1 n0 n0 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

 Decay p+ n0 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 D P The daughter nucleus: Nucleons decrease by four Charge decreases by two (Z,A)  (Z–2,A–4 ) p+ n0 The change in energy (Q): m + 2me is just the mass of a helium atom

 Decay 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 The daughter nucleus: No change in nucleons (Z,A)*  (Z,A ) D P  The change in energy (Q): 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 Decay Z A Formula for Q  +2 +4 (MP – MD – M4He)c2 – +1 0 (MP – MD)c2 e.c. –1 0 (MP – MD)c2 + –1 0 (MP – MD)c2 – 2 mec2  0 0 (MP – MD)c2 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