1. Nuclear Binding, Radioactivity Physics 1161: Pre-Lecture 33 - 34

2. 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 neutronproton Very strong force Coulomb force electron proton Strong Nuclear Force (of electron to nucleus)

3. ground state 2.2 MeV Deuterium Binding Energy

4. Nuclei have energy levels — 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

5. Comparing Nuclear and Atomic sizes Hydrogen Atom: Bohr radius = Nucleus with nucl number A: Note the TREMENDOUS difference Smaller is Bigger! Nucleus is 10 4 times smaller and binding energy is 10 5 times larger! has radius A Z

6. 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 1877.8MeV Difference is Binding energy, 2.2MeV M Deuteron = M Proton + M Neutron – |Binding Energy| proton: mc 2 =(1.67x10 -27 kg)(3x10 8 m/s) 2 =1.50x10 -10 J

7. Iron (Fe) is 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

8.  particles: nuclei   particles: electrons  : photons (more energetic than x-rays) penetrate! 3 Types of Radioactivity Easily Stopped Stopped by metal 26 Radioactive sources B field into screen detector

9.  : example recall  : example Decay Rules 1)Nucleon Number is conserved. 2)Atomic Number (charge) is conserved. 3)Energy and momentum are conserved.  : example 1)238 = 234 + 4Nucleon number conserved 2)92 = 90 + 2Charge conserved Needed to conserve momentum.

10. time Decay Function

11. 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”

12. 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/gram of Carbon.

13. Summary Nuclear Reactions –Nucleon number conserved –Charge conserved –Energy/Momentum conserved –  particles = nucleii –  - particles = electrons –  particles = high-energy photons Decays –Half-Life is time for ½ of atoms to decay Survival: