Physics 102: Lecture 27 Nuclear Binding, Radioactivity Make sure your grade book entries are correct e.g. HOUR EXAM EX / AB! Ex=excused / AB=0 (absent, no excuse) Please fill out on-line ICES forms Physics 102: Lecture 27, Slide 1
Strong Nuclear Force Hydrogen atom: Binding energy =13.6eV (of electron to nucleus) Coulomb force proton electron neutron Simplest Nucleus: Deuteron=neutron+proton proton Very strong force Binding energy of deuteron = 2.2 10 6 ev or 2.2Mev! That s around 200,000 times bigger! Physics 102: Lecture 27, Slide 2
Deuterium Binding Energy 2.2 MeV ground state Physics 102: Lecture 27, Slide 3
Physics 102: Lecture 27, Slide 4
Nuclei have energy level just like atoms energy needed to remove a neutron from 12 C is 18.7 MeV energy needed to remove a proton from 12 C is 16.0 MeV 12 C energy levels Note the energy scale is MeV rather than ev Physics 102: Lecture 27, Slide 5
Smaller is Bigger! Comparing Nuclear and Atomic sizes Hydrogen Atom: Bohr radius = 5.29 10 11 m Nucleus with nucl number A: A Z Physics 102: Lecture 27, Slide 6 27 13 Al has radius r A 1/3 (1.2 10 15 m) r 3.6 10 15 m Note the TREMENDOUS difference Nucleus is 10 4 times smaller and binding energy is 10 5 times larger!
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 7
Physics 102: Lecture 27, Slide 8
Binding Energy Einstein s famous equation E = m c 2 proton: mc 2 =(1.67x10-27 kg)(3x10 8 m/s) 2 =1.50x10-10 J Proton: mc 2 = 938.3MeV Neutron: mc 2 = 939.5MeV Adding these, get 1877.8MeV Deuteron: mc 2 =1875.6MeV Physics 102: Lecture 27, Slide 9 Difference is Binding energy, 2.2MeV M Deuteron = M Proton + M Neutron Binding Energy
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 10
Iron (Fe) is most binding energy/nucleon. Lighter have too few nucleons, heavier have too many. 10 Binding Energy Plot BINDING ENERGY in MeV/nucleon Fusion Fission 238 92U Fission = Breaking large atoms into small Fusion = Combining small atoms into large Physics 102: Lecture 27, Slide 11
Physics 102: Lecture 27, Slide 12
Preflight 27.3 Which element has the highest binding energy/nucleon? Neon (Z=10) Iron (Z=26) Iodine (Z=53) Physics 102: Lecture 27, Slide 13
Preflight 27.4 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 For Fe, B.E./nucleon 9MeV 56 26Fe has 56 nucleons Total B.E 56x9=504 MeV Physics 102: Lecture 27, Slide 14
3 Types of Radioactivity B field into screen α particles: 4 2He nuclei Easily Stopped β particles: electrons γ : photons (more energetic than x-rays) penetrate! Physics 102: Lecture 27, Slide 15 Radioactive sources detector Stopped by metal
Physics 102: Lecture 27, Slide 16
Decay Rules 1) Nucleon Number is conserved. 2) Atomic Number (charge) is conserved. 3) Energy and momentum are conserved. α: example 238 92U 234 90 Th +α recall 4 2He =α 1) 238 = 234 + 4 Nucleon number conserved 2) 92 = 90 + 2 Charge conserved β: example 1 1 + 0 0n 1p 1 A * A γ: example P P+ γ Z Z e ν 0 + 0 0 0 Needed to conserve momentum. Physics 102: Lecture 27, Slide 17
Preflight 27.6 A nucleus undergoes α 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 Physics 102: Lecture 27, Slide 18
Preflight 27.7 234 90Th 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. β Physics 102: Lecture 27, Slide 19
Physics 102: Lecture 27, Slide 20
ACT: Decay Which of the following decays is NOT allowed? 1 2 3 4 238 92U 234 90 Th +α 210 84 Po 82Pb+ 214 14 C 14 6 7N + γ 40 40 0 0 19 20 1 0 4 2 K P+ e + ν He Physics 102: Lecture 27, Slide 21
Preflight 27.8 Decays per second, or activity ΔN Δt = λn decay constant No. of nuclei present 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 Physics 102: Lecture 27, Slide 22
ACT: Radioactivity Decays per second, or activity ΔN Δt = λn decay constant No. of nuclei present Start with 16 14 C atoms. After 6000 years, there are only 8 left. How many will be left after another 6000 years? 1) 0 2) 4 3) 8 Physics 102: Lecture 27, Slide 23
Physics 102: Lecture 27, Slide 24
Decay Function N(t ) = N 0 e λt t T = N 0 2 1/2 Physics 102: Lecture 27, Slide 25 time
Radioactivity Quantitatively Decays per second, or activity Survival: ΔN Δt = λn decay constant N(t ) = N 0 e λt No. of nuclei present Instead of base e we can use base 2: e λt = 2 Physics 102: Lecture 27, Slide 26 No. of nuclei present at time t No. we started with at t=0 t T 1/2 where T1/2 = 0.693 λ Half life Then we can write N(t ) = N 0 e λt t = N 0 2 T 1/2
You are radioactive! One in 8.3x10 11 carbon atoms is 14 C which β decays with a ½ life of 5730 years. Determine # of decays/gram of Carbon. N 14 1.0 12 mole g 1 8.3 10 ( 23 6.02 10 ) = 11 = 6 10 10 atoms g λ =.693 = T 1/ 2. 693 12 s -1 5730 365 24 60 60 = 3.83 10 ΔN Δt = λn Physics 102: Lecture 27, Slide 27 = 0.23 decays/s
Physics 102: Lecture 27, Slide 28
Carbon Dating We just determined that living organisms should have a decay rate of about 0.23 events/ gram of carbon. The bones of an ice man are found to have a decay rate of 0.23/ 2 events/gram. We can estimate he died about 6000 years ago. Physics 102: Lecture 27, Slide 29
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 30
Summary Nuclear Reactions Nucleon number conserved Charge conserved Energy/Momentum conserved α particles = 4 nucleii 2He β - particles = electrons γ particles = high-energy photons Survival: N(t ) = N 0 e λt T 1/2 = 0.693 λ Decays Half-Life is time for ½ of atoms to decay Physics 102: Lecture 27, Slide 31
Physics 102: Lecture 27, Slide 32
See you next time! Take a look at Special Relativity in 14 Easy (Hyper)lessons: http://web.hep.uiuc.edu/home/g-gollin/relativity/ Physics 102: Lecture 27, Slide 33
Physics 102: Lecture 27, Slide 34