IB Physics 12 Nuclear Physics IV Mr. Jean

The plan: Video clip of the day Beta & Gamma Decay Models Practice Questions Time to work on Quest Questions

Decay Reviews: Q83sr4 (ALPHA) (first 6 minutes) Q83sr4 K2Cj62Y (BETA) (first 10 minutes) K2Cj62Y 3xJSJE (GAMMA) (first 13 minutes) 3xJSJE

Gamma and Beta decays are similar A Family of Four Force Carriers β decay γ decay Unlike α decay, β and γ decays are closely related (e.g. like cousins). They often occur together as in the typical decay scheme (i.e. 198 Au) They just involved changes in nucleon states (p n, n p, p p) They involve the same basic force (γ, W ± ) carrier but in different state But β decays are generally much slower (~100,000) than γ decays (produced by EM force) because the Ws are heavy particles (which makes force weaker) N N

Gamma and Beta decays are very similar Gamma Decay Internal Conversion Electron Capture Pair Internal Conversion β + Decay β - Decay EM weak EM weak Nucleon + One Lepton Nucleon + Two Leptons Nucleon + Zero Leptons Decay Name of process Interaction Out Channel

p n BETA PLUS DECAYBETA MINUS DECAY n p PAIR INTERNAL CONVERSION p’ p Feynman Diagrams - Similarity TIME All these decay types are similar in structure They all have a 4 point vertex They all have 3 particles in the final state The fact that the Q of the decay is shared between 3 particles means that the outgoing observed particle [ie. electron or positron] has a spectrum of energies in the range (0 to Q). OUT CHANNEL ---- One nucleon + 2 leptons

n p INTERNAL CONVERSION ELECTRON CAPTURE [Mono-energetic electrons ][Mono-energetic neutrinos] Feynman Diagrams - Similarity TIME  p GAMMA DECAY p’ p [Mono-energetic photons ] p’ All these decays have only two particles in their output state. The Q of the decay is shared between only 2 particles Conservation of Energy: The emitted particle ( γ, e -, ν e ) is monoenergetic. OUT CHANNEL ---- One nucleon + 1 lepton

BETA PLUS DECAYBETA MINUS DECAYPAIR INTERNAL CONVERSION Quark level Feynman Diagrams - Similarity TIME duddud duuduu duuduu duddud duuduu duuduu The proton is made of 3 quarks – uud (up, up, down) The neutron is made also of 3 quarks - udd (up, down, down) We see the very close similarity of pattern between reactions through W and γ particles. NOTE: only vertices of 3 particles are now seen (makes sense)

INTERNAL CONVERSION ELECTRON CAPTURE Quark level Feynman Diagrams - Similarity TIME  GAMMA DECAY duddud duuduu duuduu duuduu duuduu duuduu Again we see that there are ONLY 3 PARTICLE – VERTICES We see the similarity of the decays are propogated through the intermedicate “Force” particles (W and γ). Remember in INTERNAL CONV. And ELECTRON CAPTURE the electron comes from the core electron orbitals of THE ATOM.

Radioactive Materials The rate of decay for radioactive substances is expressed in terms of the activity R, given by: Activity N = Number of undecayed nuclei One curie (Ci) is the activity of a radioactive material that decays at the rate of 3.7 x Bq or 3.7 x disintegrations per second. One becquerel (Bq) is an activity equal to one disintegration per second (1 s -1 ).

The Half-Life The half-life T 1/2 of an isotope is the time in which one- half of its unstable nuclei will decay. NoNo Number of Half-lives Number Undecayed Nuclei 1432 Where n is number of half-lives

Example: Radium-226 has a half-life of 1620 years. This is shown in the graph below. One kg of radium-226 begins the thing. After one half-life (1620years) only half of the sample remains – the other half has decayed into some other element. After two half-lives only one fourth would remain and so on.

Half-Life (Cont.) The same reasoning will apply to activity R or to amount of material. In general, the following three equations can be applied to radioactivity: Nuclei Remaining Activity R Mass Remaining Number of Half-lives:

Example 6: A sample of iodine-131 has an initial activity of 5 mCi. The half-life of I-131 is 8 days. What is the activity of the sample 32 days later? First we determine the number of half-lives: n = 4 half-lives R = mCi There would also be 1/16 remaining of the mass and 1/16 of the number of nuclei.

To do: Work on Quest Assignment Review and Study Decay Models Read about Feynman Models