3. IB Assessment Statements Topic 13.2, Nuclear Physics 13.2.1.Explain how the radii of nuclei may be estimated from charged particle scattering experiments. 13.2.2.Describe how the masses of nuclei may be determined using a Bainbridge mass spectrometer. 13.2.3.Describe one piece of evidence for the existence of nuclear energy levels.

4. IB Assessment Statements Topic 13.2, Nuclear Physics 13.2.4.Describe β + decay, including the existence of the neutrino. 13.2.5.State the radioactive decay law as an exponential function and define the decay constant. 13.2.6.Derive the relationship between decay constant and half-life.

5. IB Assessment Statements Topic 13.2, Nuclear Physics 13.2.7.Outline methods for measuring the half- life of an isotope. 13.2.8.Solve problems involving radioactive half-life.

6. Objectives  Solve problems of closest approach using the law of conservation of energy and appreciate that nuclei have well-defined radii  Describe a mass spectrometer and its implications for isotope existence  State theoretical arguments that have been used to postulate the existence of the neutrino

7. Objectives  State the radioactive decay law,  State the meaning of half-life and decay constant and derive the relationship between them

8. Objectives  Appreciate that the decay constant is the probability of decay per unit time  Understand that the initial activity of a sample is,  Obtain short and long half-lives from experimental data

9. Objectives  Solve problems with activities and the radioactive decay law

10. Scattering Experiments and Distance of Closest Approach  An alpha particle of charge q=+2e is fired head-on at a nucleus  The particle’s total energy is kinetic, E=E k

11. Scattering Experiments and Distance of Closest Approach  The particle is repelled by the positive charge of the nucleus

12. Scattering Experiments and Distance of Closest Approach  When the particle stops, all of its kinetic energy has been converted into potential energy

13. Scattering Experiments and Distance of Closest Approach  When the particle stops, all of its kinetic energy has been converted into potential energy

14. Scattering Experiments and Distance of Closest Approach  As kinetic energy of the alpha particle increases, distance decreases until the nuclear radius is reached

15. Scattering Experiments and Distance of Closest Approach  Rutherford Scattering  http://hyperphysics.phy- astr.gsu.edu/hbase/hframe.html http://hyperphysics.phy- astr.gsu.edu/hbase/hframe.html  Closest Approach to Nucleus  http://hyperphysics.phy- astr.gsu.edu/hbase/hframe.html http://hyperphysics.phy- astr.gsu.edu/hbase/hframe.html  Nuclear Radius Relationship  http://hyperphysics.phy- astr.gsu.edu/hbase/hframe.html http://hyperphysics.phy- astr.gsu.edu/hbase/hframe.html

16. Scattering Experiments and Distance of Closest Approach  Further experiments have been able to refine the estimates for nuclear radii to be

17. Mass Spectrometer Positive ions pass through a combination magnetic and electric field so that only ones with a certain velocity will pass through S 2

18. Mass Spectrometer The positive ions then enter a third magnetic field which causes the ion to take a circular path, the radius of which is determined by its mass.

19. Mass Spectrometer  Given the same velocity, particles with a greater mass will have greater kinetic energy and thus a larger radius of curvature  Existence of isotopes was found using a mass spectrometer

20. Beta Decay and the Neutrino  Decay of a neutron  Decays into a proton, electron, and an antineutrino  This happens to free neutrons outside the nucleus because neutrons have greater mass than protons  Half-life is about 11 minutes

21. Beta Decay and the Neutrino  Decay of a proton  Decays into a neutron with the emission of a positron (anti-particle of an electron) and a neutrino  Decay occurs inside the nucleus where binding energy makes up for the mass difference  Not a split, but a disappearance and reformation

22. Beta Decay and the Neutrino  Presence of neutrinos predicted because the mass of a neutron is greater than the sum of the mass of a proton and electron

23. Beta Decay and the Neutrino  In other decays, this mass difference showed up in kinetic energy of the particles

24. Beta Decay and the Neutrino  Absence of the kinetic energy led to experiments that uncovered the neutrino (little neutral one) in 1953

25. Beta Decay and the Neutrino  Electron Capture  A proton inside the nucleus captures an electron and turns into a neutron and neutrino  This is the process occurring in neutron stars  Huge pressure inside the star drives electrons into protons, turning them into neutrons

26. Beta Decay and the Neutrino  Examples of Beta Decay

27. Nuclear Energy Levels  The nucleus, like the atom, exists in discrete energy levels  Main evidence is that alpha particles and gamma ray photons are emitted in discrete energy levels during decays  In beta decays, the electrons have a continuous range of energies

28. Nuclear Energy Levels  Nuclear energy levels of  Shown is a gamma decay (release of a photon) with energy

29. Nuclear Energy Levels  Two decays of plutonium into uranium with release of an alpha particle

30. Radioactive Decay Law  The number of nuclei that will decay per second is proportional to the number of atoms present that have not yet decayed  λ is a constant known as the decay constant  Represents the probability of decay per unit time

31. Radioactive Decay Law  The number of undecayed nuclei N at any given time in relation to the original number of undecayed nuclei N 0 is given by the equation,  The decay rate is exponential

32. Radioactive Decay Law  The derivation to the right gives the relationship between half-life and decay rate

33. Radioactive Decay Law

34.  The number of decays per second is called the activity,  The initial activity is

35. Radioactive Decay Law  The decay constant represents the probability of decay per unit time

36. Σary Review  Can you solve problems of closest approach using the law of conservation of energy and appreciate that nuclei have well-defined radii?  Can you describe a mass spectrometer and its implications for isotope existence?  Can you state theoretical arguments that have been used to postulate the existence of the neutrino?

37. Σary Review  Can you state the radioactive decay law, ?  Can you state the meaning of half-life and decay constant and derive the relationship between them?

38. Σary Review  Do you appreciate that the decay constant is the probability of decay per unit time?  Do you understand that the initial activity of a sample is, ?  Can you obtain short and long half-lives from experimental data?

39. Σary Review  Can you solve problems with activities and the radioactive decay law?

40. IB Assessment Statements Topic 13.2, Nuclear Physics 13.2.1.Explain how the radii of nuclei may be estimated from charged particle scattering experiments. 13.2.2.Describe how the masses of nuclei may be determined using a Bainbridge mass spectrometer. 13.2.3.Describe one piece of evidence for the existence of nuclear energy levels.

41. IB Assessment Statements Topic 13.2, Nuclear Physics 13.2.4.Describe β + decay, including the existence of the neutrino. 13.2.5.State the radioactive decay law as an exponential function and define the decay constant. 13.2.6.Derive the relationship between decay constant and half-life.

42. IB Assessment Statements Topic 13.2, Nuclear Physics 13.2.7.Outline methods for measuring the half- life of an isotope. 13.2.8.Solve problems involving radioactive half-life.