General Physics (PHY 2140) Lecture 37 Modern Physics Nuclear Physics Radioactivity Nuclear reactions http://www.physics.wayne.edu/~apetrov/phy2140/ Chapter 29 1
Lightning Review Last lecture: 1. Nuclear physics Properties of nuclei Binding energy, types of radiation A X Z r = r A 0 1/3 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? 2
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 4 He 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 3
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 ( ) N = λn t 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 R N = = λn t 4
Decay Curve The decay curve follows the equation N = N e λt The half-life life is also a useful parameter The half-life life is defined as the time it takes for half of any given number of radioactive nuclei to decay 0 T 1 2 = ln 2 λ = 0.693 λ 5
Units The unit of activity, R, is the Curie, Ci 1 Ci = 3.7 x 10 10 decays/second The SI unit of activity is the Becquerel, Bq 1 Bq = 1 decay / second Therefore, 1 Ci = 3.7 x 10 10 Bq The most commonly used units of activity are the mci and the µci 6
QUICK QUIZ What fraction of a radioactive sample has decayed after two halflives have elapsed? (a) 1/4 (b) 1/2 (c) 3/4 (d) not enough information to say (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: 1 1 1 3 + = 2 2 2 4 7
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 8
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 A A 4 Z X Z 2Y+ He X is called the parent nucleus Y is called the daughter nucleus 4 2 9
Alpha Decay -- Example Decay of 226 Ra 222 88 Ra 86Rn+ 226 4 2 He Half life for this decay is 1600 years Excess mass is converted into kinetic energy Momentum of the two particles is equal and opposite 10
QUICK QUIZ If a nucleus such as 226 Ra 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. (a). Conservation of momentum requires the momenta of the two fragments be equal in magnitude and oppositely directed. Thus, from KE = p 2 /2m, the lighter alpha particle has more kinetic energy that the more massive daughter nucleus. 11
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 12
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 13
Beta Decay Symbolically A Z A Z X X A Z+ 1 A Z 1 Y Y + ν ν is the symbol for the neutrino ν is the symbol for the antineutrino + + e e + ν To summarize, in beta decay, the following pairs of particles are emitted An electron and an antineutrino A positron and a neutrino + 14
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 s 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 n 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 12 5 B 12 6 C* C * C + + e γ + ν 12 12 6 6 The C* indicates the Carbon nucleus is in an excited state Gamma emission doesn t change either A or Z 15
Uses of Radioactivity Carbon Dating Beta decay of 14 C is used to date organic samples The ratio of 14 C to 12 C 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 16
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 17
Decay Series of 232 Th 232 Th Series starts with 232Th 232 Th Processes through a series of alpha and beta decays Ends with a stable isotope of lead, 208Pb 208 Pb 18
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 19
Problem Which of the following are possible reactions? (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. 20
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 21
Problem: nuclear reactions 7 4 Determine the product of the reaction 3 2 What is the Q value of the reaction? Li + He? + n 22
Determine the product of the reaction What is the Q value of the reaction? Li + He + n 7 4 X 3 2 Y? Given: reaction Find: Q =? 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. Number of nucleons (A): Number of protons (Z): Thus, it is B, i.e. The Q-value is then 7+ 4= X + 1 X = 10 3+ 2= Y + 0 Y = 5 Li + He B + n 7 4 10 1 3 2 5 0 ( ) ( ) 7 4 10 n 2 2 Q= m c = m + m m m c = 2.79MeV Li He B 23
Threshold Energy To conserve both momentum and energy, incoming particles must have a minimum amount of kinetic energy, called the threshold energy KE min = 1 + m M Q 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 24
QUICK QUIZ 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. (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. 25