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Nuclear Binding, Radioactivity

Physics 1161: Pre- Lecture 33 - 34. Nuclear Binding, Radioactivity. Coulomb force. proton. electron. proton. neutron. Very strong force. Binding energy of deuteron = or 2.2Mev! That’s around 200,000 times bigger!. Strong Nuclear Force. Hydrogen atom: Binding energy =13.6eV.

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Nuclear Binding, Radioactivity

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

  2. Coulomb force proton electron proton neutron Very strong force Binding energy ofdeuteron=or 2.2Mev!That’s around 200,000 times bigger! Strong Nuclear Force Hydrogen atom:Binding energy=13.6eV (of electron to nucleus) Simplest Nucleus: Deuteron=neutron+proton

  3. Deuterium Binding Energy 2.2 MeV ground state

  4. Nuclei have energy levels — just like atoms energy needed to remove a proton from 12C is 16.0 MeV energy needed to remove a neutron from 12C is 18.7 MeV 12C energy levels Note the energy scale is MeV rather than eV

  5. Hydrogen Atom: Bohr radius = Example has radius Nucleus with nucl number A: A Note the TREMENDOUS difference Z Smaller is Bigger! ComparingNuclearandAtomicsizes Nucleus is 104 times smaller and binding energy is 105 times larger!

  6. Proton: mc2 = 938.3MeV Adding these, get 1877.8MeV Neutron:mc2= 939.5MeV Binding Energy Einstein’s famous equation E = m c2 Example proton: mc2=(1.67x10-27kg)(3x108 m/s)2=1.50x10-10 J Difference is Binding energy,2.2MeV Deuteron: mc2 =1875.6MeV MDeuteron = MProton + MNeutron – |Binding Energy|

  7. Fusion Binding Energy Plot Iron (Fe) is most binding energy/nucleon. Lighter have too few nucleons, heavier have too many. 10 Fission BINDING ENERGY in MeV/nucleon Fission = Breaking large atoms into small Fusion = Combining small atoms into large

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

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

  10. Decay Function time

  11. Survival: No. of nuclei present at time t No. we started with at t=0 No. of nuclei present Decays per second, or “activity” decay constant where Half life Then we can write Radioactivity Quantitatively Instead of baseewe can use base2:

  12. Example You are radioactive! One in 8.3x1011 carbon atoms is 14C which b- decays with a ½ life of 5730 years. Determine # of decays/gram of Carbon.

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

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