Physics 102: Lecture 27, Slide 1 Nuclear Binding, Radioactivity Physics 102: Lecture 28

Physics 102: Lecture 27, Slide 2 Nucleus = Protons+ Neutrons nucleons A = nucleon number (atomic mass number) Gives you mass density of element Z = proton number (atomic number) Gives chemical properties (and name) N = neutron number A=N+Z Recall: Nuclear Physics A Z Periodic_Table

Physics 102: Lecture 27, Slide 3 A material is known to be an isotope of lead Based on this information which of the following can you specify? 1) The atomic mass number 2) The neutron number 3) The number of protons Preflight 27.1

Physics 102: Lecture 27, Slide 4 Hydrogen atom: Binding energy =13.6eV Binding energy of deuteron = or 2.2Mev! That’s around 200,000 times bigger! Simplest Nucleus: Deuteron=neutron+proton (Isotope of H) neutronproton Very strong force Coulomb force electron proton Strong Nuclear Force (of electron to nucleus)

Physics 102: Lecture 27, Slide 5 Can get 4 nucleons into n=1 state. Energy will favor N=Z Pauli Principle - neutrons and protons have spin like electron, and thus m s =  1/2. But protons repel one another (Coulomb Force) and when Z is large it becomes harder to put more protons into a nucleus without adding even more neutrons to provide more of the Strong Force. For this reason, in heavier nuclei N>Z. # protons = # neutrons 7

Physics 102: Lecture 27, Slide 6 ground state 2.2 MeV Deuteron Binding Energy

Physics 102: Lecture 27, Slide 7 Nuclei have energy level (just like atoms) 12 C energy levels Note the energy scale is MeV rather than eV energy needed to remove a proton from 12 C is 16.0 MeV energy needed to remove a neutron from 12 C is 18.7 MeV

Physics 102: Lecture 27, Slide 8 Preflight 27.2 Where does the energy released in the nuclear reactions of the sun come from? (1)covalent bonds between atoms (2)binding energy of electrons to the nucleus (3)binding energy of nucleons

Physics 102: Lecture 27, Slide 9 Binding Energy Einstein’s famous equation E = m c 2 Proton: mc 2 = 938.3MeV Neutron: mc 2 = 939.5MeV Deuteron: mc 2 =1875.6MeV Adding these, get MeV Difference is Binding energy, 2.2MeV M Deuteron = M Proton + M Neutron – |Binding Energy| proton: mc 2 =(1.67x kg)(3x10 8 m/s) 2 =1.50x J

Physics 102: Lecture 27, Slide 10 ACT: Binding Energy Which system “weighs” more? 1)Two balls attached by a relaxed spring. 2)Two balls attached by a stretched spring. 3)They have the same weight.

Physics 102: Lecture 27, Slide 11 Iron (Fe) has most binding energy/nucleon. Lighter have too few nucleons, heavier have too many. BINDING ENERGY in MeV/nucleon 10 Binding Energy Plot Fission Fusion Fusion = Combining small atoms into large Fission = Breaking large atoms into small

Physics 102: Lecture 27, Slide 12 Neon (Z=10) Iron (Z=26) Iodine (Z=53) Which element has the highest binding energy/nucleon? Preflight 27.3

Physics 102: Lecture 27, Slide 13 Which of the following is most correct for the total binding energy of an Iron atom (Z=26)? 9 MeV 234 MeV 270 MeV 504 Mev Preflight 27.4

Physics 102: Lecture 27, Slide 14  particles: nuclei   particles: electrons  : photons (more energetic than x-rays) penetrate! 3 Types of Radioactivity Easily Stopped Stopped by metal Radioactive sources B field into screen detector

Physics 102: Lecture 27, Slide 15  : example recall  : example Decay Rules 1)Nucleon Number (A) is conserved. 2)Atomic Number (Z) is conserved. 3)Energy and momentum are conserved.  : example 1)238 = Nucleon number conserved 2)92 = Charge conserved Needed to conserve momentum.

Physics 102: Lecture 27, Slide 16 A nucleus undergoes  decay. Which of the following is FALSE? 1. Nucleon number decreases by 4 2. Neutron number decreases by 2 3. Charge on nucleus increases by 2 Preflight 27.6

Physics 102: Lecture 27, Slide 17 The nucleus undergoes decay. Which of the following is true? 1. The number of protons in the daughter nucleus increases by one. 2. The number of neutrons in the daughter nucleus increases by one. Preflight 27.7

Physics 102: Lecture 27, Slide 18 ACT: Decay Which of the following decays is NOT allowed?

Physics 102: Lecture 27, Slide 19 If the number of radioactive nuclei present is cut in half, how does the activity change? 1) It remains the same 2) It is cut in half 3) It doubles No. of nuclei present decay constant Decays per second, or “activity” Radioactive decay rates Preflight 27.8

Physics 102: Lecture 27, Slide 20 ACT: Radioactivity Start with C atoms. After 6000 years, there are only 8 left. How many will be left after another 6000 years? 1) 02) 43) 8 No. of nuclei present decay constant Decays per second, or “activity”

Physics 102: Lecture 27, Slide 21 time Decay Function

Physics 102: Lecture 27, Slide 22 Instead of base e we can use base 2: Survival: No. of nuclei present at time t No. we started with at t=0 where Then we can write Half life Radioactivity Quantitatively No. of nuclei present decay constant Decays per second, or “activity”

Physics 102: Lecture 27, Slide 23 You are radioactive! One in 8.3x10 11 carbon atoms is 14 C which   decays with a ½ life of 5730 years. Determine # of decays/s per gram of Carbon.

Physics 102: Lecture 27, Slide 24 Carbon Dating We just determined that living organisms should have a decay rate of about 0.23 events/s per gram of carbon. The bones of an ice man are found to have a decay rate of 0.23/2 events/s per gram. We can estimate he died about 6000 years ago.

Physics 102: Lecture 27, Slide 25 ACT/Preflight 27.9 The half-life for beta-decay of 14 C is ~6,000 years. You test a fossil and find that only 25% of its 14 C is un-decayed. How old is the fossil? 1. 3,000 years 2. 6,000 years 3. 12,000 years

Physics 102: Lecture 27, Slide 26 Summary Nuclear Reactions –Nucleon number conserved –Charge conserved –Energy/Momentum conserved –  particles = nuclei –  - particles = electrons –  particles = high-energy photons Decays –Half-Life is time for ½ of atoms to decay Survival: