General Physics (PHY 2140)

1. General Physics (PHY 2140) Lecture 37 • Modern Physics • Nuclear Physics • Radioactivity • Nuclear reactions http://www.physics.wayne.edu/~apetrov/PHY2140/ Chapter 29

2. Lightning Review • Last lecture: • Nuclear physics • Properties of nuclei • Binding energy, types of radiation Review Problem: An alpha particle has twice the charge of a beta particle. Why does the former deflect less than the latter when passing between electrically charged plates, assuming that both have the same speed?

3. 29.3 Radioactivity • Radioactivity is the spontaneous emission of radiation • Experiments suggested that radioactivity was the result of the decay, or disintegration, of unstable nuclei • Three types of radiation can be emitted • Alpha particles • The particles are 4He nuclei • Beta particles • The particles are either electrons or positrons • A positron is the antiparticle of the electron • It is similar to the electron except its charge is +e • Gamma rays • The “rays” are high energy photons

4. The Decay Constant • The number of particles that decay in a given time is proportional to the total number of particles in a radioactive sample • λ is called the decay constant and determines the rate at which the material will decay • The decay rate or activity, R, of a sample is defined as the number of decays per second

5. Decay Curve • The decay curve follows the equation • The half-life is also a useful parameter • The half-life is defined as the time it takes for half of any given number of radioactive nuclei to decay

6. Units • The unit of activity, R, is the Curie, Ci • 1 Ci = 3.7 x 1010 decays/second • The SI unit of activity is the Becquerel, Bq • 1 Bq = 1 decay / second • Therefore, 1 Ci = 3.7 x 1010 Bq • The most commonly used units of activity are the mCi and the µCi

7. What fraction of a radioactive sample has decayed after two half-lives have elapsed? (a) 1/4 (b) 1/2 (c) 3/4 (d) not enough information to say QUICK QUIZ (c). At the end of the first half-life interval, half of the original sample has decayed and half remains. During the second half-life interval, half of the remaining portion of the sample decays. The total fraction of the sample that has decayed during the two half-lives is:

8. 29.4 The Decay Processes – General Rules • When one element changes into another element, the process is called spontaneous decay or transmutation • The sum of the mass numbers, A, must be the same on both sides of the equation • The sum of the atomic numbers, Z, must be the same on both sides of the equation • Conservation of mass-energy and conservation of momentum must hold

9. Alpha Decay • When a nucleus emits an alpha particle it loses two protons and two neutrons • N decreases by 2 • Z decreases by 2 • A decreases by 4 • Symbolically • X is called the parent nucleus • Y is called the daughter nucleus

10. Alpha Decay -- Example • Decay of 226Ra • Half life for this decay is 1600 years • Excess mass is converted into kinetic energy • Momentum of the two particles is equal and opposite

11. If a nucleus such as226Ra that is initially at rest undergoes alpha decay, which of the following statements is true? (a) The alpha particle has more kinetic energy than the daughter nucleus. (b) The daughter nucleus has more kinetic energy than the alpha particle. (c) The daughter nucleus and the alpha particle have the same kinetic energy. QUICK QUIZ (a). Conservation of momentum requires the momenta of the two fragments be equal in magnitude and oppositely directed. Thus, from KE = p2/2m, the lighter alpha particle has more kinetic energy that the more massive daughter nucleus.

12. Beta Decay • During beta decay, the daughter nucleus has the same number of nucleons as the parent, but the atomic number is one less • In addition, an electron (positron) was observed • The emission of the electron is from the nucleus • The nucleus contains protons and neutrons • The process occurs when a neutron is transformed into a proton and an electron • Energy must be conserved

13. Beta Decay – Electron Energy • The energy released in the decay process should almost all go to kinetic energy of the electron • Experiments showed that few electrons had this amount of kinetic energy • To account for this “missing” energy, in 1930 Pauli proposed the existence of another particle • Enrico Fermi later named this particle the neutrino • Properties of the neutrino • Zero electrical charge • Mass much smaller than the electron, probably not zero • Spin of ½ • Very weak interaction with matter

14. Beta Decay • Symbolically •  is the symbol for the neutrino • is the symbol for the antineutrino • To summarize, in beta decay, the following pairs of particles are emitted • An electron and an antineutrino • A positron and a neutrino

15. Gamma Decay • Gamma rays are given off when an excited nucleus “falls” to a lower energy state • Similar to the process of electron “jumps” to lower energy states and giving off photons • The excited nuclear states result from “jumps” made by a proton or neutron • The excited nuclear states may be the result of violent collision or more likely of an alpha or beta emission • Example of a decay sequence • The first decay is a beta emission • The second step is a gamma emission • The C* indicates the Carbon nucleus is in an excited state • Gamma emission doesn’t change either A or Z

16. Uses of Radioactivity • Carbon Dating • Beta decay of 14C is used to date organic samples • The ratio of 14C to 12C is used • Smoke detectors • Ionization type smoke detectors use a radioactive source to ionize the air in a chamber • A voltage and current are maintained • When smoke enters the chamber, the current is decreased and the alarm sounds • Radon pollution • Radon is an inert, gaseous element associated with the decay of radium • It is present in uranium mines and in certain types of rocks, bricks, etc that may be used in home building • May also come from the ground itself

17. 29.5 Natural Radioactivity • Classification of nuclei • Unstable nuclei found in nature • Give rise to natural radioactivity • Nuclei produced in the laboratory through nuclear reactions • Exhibit artificial radioactivity • Three series of natural radioactivity exist • Uranium • Actinium • Thorium

18. Decay Series of 232Th • Series starts with 232Th • Processes through a series of alpha and beta decays • Ends with a stable isotope of lead, 208Pb

19. 29.6 Nuclear Reactions • Structure of nuclei can be changed by bombarding them with energetic particles • The changes are called nuclear reactions • As with nuclear decays, the atomic numbers and mass numbers must balance on both sides of the equation

20. Which of the following are possible reactions? Problem (a) and (b). Reactions (a) and (b) both conserve total charge and total mass number as required. Reaction (c) violates conservation of mass number with the sum of the mass numbers being 240 before reaction and being only 223 after reaction.

21. Q Values • Energy must also be conserved in nuclear reactions • The energy required to balance a nuclear reaction is called the Q value of the reaction • An exothermic reaction • There is a mass “loss” in the reaction • There is a release of energy • Q is positive • An endothermic reaction • There is a “gain” of mass in the reaction • Energy is needed, in the form of kinetic energy of the incoming particles • Q is negative

22. Problem: nuclear reactions Determine the product of the reaction What is the Q value of the reaction?

23. Determine the product of the reaction What is the Q value of the reaction? In order to balance the reaction, the total amount of nucleons (sum of A-numbers) must be the same on both sides. Same for the Z-number. Given: reaction Find: Q = ? Number of nucleons (A): Number of protons (Z): Thus, it is B, i.e. The Q-value is then

24. Threshold Energy • To conserve both momentum and energy, incoming particles must have a minimum amount of kinetic energy, called the threshold energy • m is the mass of the incoming particle • M is the mass of the target particle • If the energy is less than this amount, the reaction cannot occur

25. If the Q value of an endothermic reaction is -2.17 MeV, the minimum kinetic energy needed in the reactant nuclei if the reaction is to occur must be (a) equal to 2.17 MeV, (b) greater than 2.17 MeV, (c) less than 2.17 MeV, or (d) precisely half of 2.17 MeV. QUICK QUIZ (b). In an endothermic reaction, the threshold energy exceeds the magnitude of the Q value by a factor of (1+ m/M), where m is the mass of the incident particle and M is the mass of the target nucleus.