Nuclear Binding, Radioactivity

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

2 Recall: Nuclear Physics A Z 6 3 Li Nucleus = Protons+ Neutrons nucleons Z = proton number (atomic number) Gives chemical properties (and name) N = neutron number A = nucleon number (atomic mass number) Gives you mass density of element Physics 102: Lecture 27, Slide 2 A=N+Z Periodic_Table

3 Preflight 27.1 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 Physics 102: Lecture 27, Slide 3

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

5 # protons = # neutrons Pauli Principle - neutrons and protons have spin like electron, and thus m s = ±1/2. n n p p n n p p Can get 4 nucleons into n=1 state. Energy will favor N=Z 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. Physics 102: Lecture 27, Slide 5 7

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

7 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 Physics 102: Lecture 27, Slide 7 12 C energy levels Note the energy scale is MeV rather than ev

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 8

9 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 MeV 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

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 10

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

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 12

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 Physics 102: Lecture 27, Slide 13

14 3 Types of Radioactivity B field into screen Radioactive sources α particles: 4 2He nuclei β particles: electrons detector Easily Stopped Stopped by metal Physics 102: Lecture 27, Slide 14 γ : photons (more energetic than x-rays) penetrate!

15 Decay Rules 1) Nucleon Number (A) is conserved. 2) Atomic Number (Z) is conserved. 3) Energy and momentum are conserved. α: example U Th +α recall 4 2He =α 1) 238 = Nucleon number conserved 2) 92 = Charge conserved β: example n 1p 1 A * A γ: example P P+ γ Z Z e ν Needed to conserve momentum. Physics 102: Lecture 27, Slide 15

16 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 16

17 Preflight Th 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 17

18 ACT: Decay Which of the following decays is NOT allowed? U Th +α Po 82Pb C N + γ K P+ e + ν He Physics 102: Lecture 27, Slide 18

19 Radioactive decay rates 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 Preflight 27.8 Physics 102: Lecture 27, Slide 19

20 ACT: Radioactivity Decays per second, or activity ΔN Δt = λn decay constant No. of nuclei present Start with 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 20

21 Decay Function N(t ) = N 0 e λt t T = N 0 2 1/2 Physics 102: Lecture 27, Slide 21 time

22 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: Physics 102: Lecture 27, Slide 22 e λt = 2 No. of nuclei present at time t No. we started with at t=0 t T 1/2 where T1/2 = λ Half life Then we can write N(t ) = N 0 e λt t = N 0 2 T 1/2

23 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 25

24 Summary Nuclear Reactions Nucleon number conserved Charge conserved Energy/Momentum conserved α particles = 4 2He nuclei β - particles = electrons γ particles = high-energy photons Survival: N(t ) = N 0 e λt T 1/2 = λ Decays Half-Life is time for ½ of atoms to decay Physics 102: Lecture 27, Slide 26

Nuclear Binding, Radioactivity

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