Chapter 30 Nuclear Physics

1. Chapter 30 Nuclear Physics AP Physics B Lecture Notes

2. Nuclear Physics Sections 29-01 Some Properties of Nuclei 29-02 Binding Energy 29-03 Radioactivity 29-04 The Decay Process

3. Some Properties of Nuclei The size of the nucleus The nucleus: Atomic mass protons + neutrons Chemical symbol Atomic number Protons Number of neutrons = A - Z Nuclear Physics 30

4. Some Properties of Nuclei Proton has positive charge: Neutron is electrically neutral: The radius of the nucleus Atomic mass unit Nucleus is made of protons and neutrons Nuclear Physics 30

5. Chapter 29: Nuclear Physics An atom's atomic number is determined by the number of (A) neutrons in its nucleus. (B) nucleons in its nucleus. (C) protons in its nucleus. (D) alpha particles in its nucleus.

6. Some Properties of Nuclei From the following table, you can see that the electron is considerably less massive than a nucleon. Nuclear Physics 30

7. Chapter 29: Nuclear Physics If an atom's atomic number is given by Z, its atomic mass by A, and its neutron number by N, which of the following is correct? (A) N = A - Z (B) N = Z - A (C) N = A + Z (D) none of the given answers

8. Binding Energy P P N P N N P N An Alpha particle The total mass of a stable nucleus is always less than the sum of the masses of its separate protons and neutrons. Nuclear Physics 30

9. Binding Energy Energy released This difference between the total mass of the constituents and the mass of the nucleus is called the total binding energy of the nucleus. Binding energy Nuclear Physics 30

10. Binding Energy To compare how tightly bound different nuclei are, we divide the binding energy by A to get the binding energy per nucleon. The higher the binding energy per nucleon, the more stable the nucleus. Nuclear Physics 30

11. Binding Energy More massive nuclei require extra neutrons to overcome the Coulomb repulsion of the protons in order to be stable. The force that binds the nucleons together is called the strong nuclear force. It is a very strong, but short-range, force. It is essentially zero if the nucleons are more than about 10-15 m apart. Nuclear Physics 30

12. Binding Energy Calculate the binding energy per nucleon for a nucleus of

13. Binding Energy b) Calculate the total binding energy, and the binding energy per nucleon, for

14. Chapter 29: Nuclear Physics Compared to the masses of its separate protons and neutrons, the total mass of a stable nucleus is always (A) less. (B) the same. (C) greater. (D) zero.

15. Chapter 29: Nuclear Physics When nucleons join to form a stable nucleus, energy is (A) destroyed. (B) absorbed. (C) released. (D) not transferred.

16. Radioactivity Nuclei that are unstable decay; many such decays are governed by another force called the weak nuclear force. Radioactive rays were observed to be of three types: Alpha radiation are helium nuclei and can barely penetrate a piece of paper Beta radiation are electrons and can penetrate 3 mm of aluminum Gamma radiation are electromagnetic radiation and can penetrate several centimeters of lead Nuclear Physics 30

17. Radioactivity Alpha and beta rays are bent in opposite directions in a magnetic field, while gamma rays are not bent at all. Nuclear Physics 30

18. Chapter 29: Nuclear Physics Beta rays can penetrate (A) air only. (B) a piece of paper. (C) several centimeters of lead. (D) several millimeters of aluminum.

19. Chapter 29: Nuclear Physics Gamma rays can penetrate (A) air only. (B) a piece of paper. (C) several millimeters of aluminum. (D) several centimeters of lead.

20. The Decay Process Example of alpha decay: Radium-226 will alpha-decay to radon-22 Nuclear Physics 30

21. The Decay Process In general, alpha decay can be written: Alpha decay occurs when the strong nuclear force cannot hold a large nucleus together. The mass of the parent nucleus is greater than the sum of the masses of the daughter nucleus and the alpha particle; this difference is called the disintegration energy. Alpha decay is so much more likely than other forms of nuclear disintegration because the alpha particle itself is quite stable. Nuclear Physics 30

22. The Decay Process Beta decay occurs when a nucleus emits an electron. An example is the decay of carbon-14: The nucleus still has 14 nucleons, but it has one more proton and one fewer neutron. In general, beta decay can be written: The fundamental process is a neutron decaying to a proton, electron, and neutrino: Nuclear Physics 30

23. The Decay Process Beta decay can also occur where the nucleus emits a positron rather than an electron: The nucleus still has 19 nucleons, but it has one more neutron and one fewer protons. In general, positron emission can be written: The fundamental process is a proton decaying to a neutron, positron, and neutrino: Nuclear Physics 30

24. The Decay Process And a nucleus can capture one of its inner electrons: The nucleus still has 7 nucleons, but it has one more neutron and one fewer protons. In general, positron emission can be written: The fundamental process in an electron capture: Nuclear Physics 30

25. The Decay Process Gamma rays are very high-energy photons. They are emitted when a nucleus decays from an excited state to a lower state, just as photons are emitted by electrons returning to a lower state. In general, gamma emission can be written: Nuclear Physics 30

26. The Decay Process What is the maximum KE of the emitted b particle during the decay of

27. The Decay Process How much recoil energy does a nucleus get when it emits a 1.46 MeV gamma ray?

28. The Decay Process Half-Life and Rate of Decay Nuclear decay is a random process; the decay of any nucleus is not influenced by the decay of any other. The number of decays in a short time interval is proportional to the number of nuclei present and to the time: Here, l is a constant characteristic of that particular nuclide, called the decay constant. Nuclear Physics 30

29. The Decay Process Half-Life and Rate of Decay This equation can be solved, using calculus, for N as a function of time: The half-life is the time it takes for half the nuclei in a given sample to decay. It is related to the decay constant: Nuclear Physics 30

30. The Decay Process Carbon-14 has a half-life of 5730 years. What is the activity of a sample that contains 3.1 x 1020 nuclei?

31. The Decay Process What fraction of a sample is left after exactly 6 half-lives?

32. The Decay Process Phosphorus-32 has a half-life of 1.23 x 106 s. Calculate the activity of a pure 9.7 mg sample.

33. Chapter 29: Nuclear Physics Gamma rays can penetrate (A) air only. (B) a piece of paper. (C) several millimeters of aluminum. (D) several centimeters of lead.

34. Chapter 29: Nuclear Physics During β- decay (A) a neutron is transformed to a proton. (B) a proton is transformed to a neutron. (C) a neutron is ejected from the nucleus. (D) a proton is ejected from the nucleus.

35. Chapter 29: Nuclear Physics When a β+ particle is emitted from an unstable nucleus, the atomic number of the nucleus (A) increases by 1. (B) decreases by 1. (C) does not change. (D) none of the given answers

36. Summary Nuclei contain protons and neutrons – nucleons Total number of nucleons, A, is atomic mass number Number of protons, Z, is atomic number Nuclear masses are measured in u; carbon-12 is defined as having a mass of 12 u Difference between mass of nucleus and mass of its constituents is binding energy Unstable nuclei decay through alpha, beta, or gamma emission An alpha particle is a helium nucleus; a beta particle is an electron or positron; a gamma ray is a highly energetic photon Nuclear Physics 30

37. Summary The number of decays per unit time is proportional to the number of nuclei present: Nuclei are held together by the strong nuclear force; the weak nuclear force is responsible for beta decay Electric charge, linear and angular momentum, mass-energy, and nucleon number are all conserved Radioactive decay is a statistical process The half-life is the time it takes for half the nuclei to decay Nuclear Physics 30

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