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Physics 11 (Fall 2012) Chapter 30: Nuclear Physics “You've got a lot of choices. If getting out of bed in the morning is a chore and you're not smiling on a regular basis, try another choice.” – Steven D. Woodhull “The greater part of our happiness or misery depends on our dispositions, and not our circumstances.” – Martha Washington Reading: pages 991 – 1017 Outline: ⇒ structure of nuclei atomic number Z and atomic mass number A isotopes ⇒ nuclear stability (PowerPoint) strong nuclear force binding energy mass defect ⇒ radiation and radioactivity alpha, beta, and gamma decay the neutrino (PowerPoint) ⇒ nuclear decay and half-lives half-life and decay constant radioactive decay and activity radioactive carbon dating (read on your own) ⇒ the ultimate building blocks of matter (read on your own) Problem Solving Chemical elements are often written with the shorthand notation ZA X where A is the number of protons plus neutrons, Z is the number of protons, and X is the chemical symbol for the element. To find the binding energy of a nucleus, use binding energy B = ( Δm )c2 where Δm is the difference in mass (mass defect) between the nucleus and the mass of the protons plus neutrons. If masses are given in atomic mass units, then you can use B = ( Δm ) × 931.5 MeV/u. Some problems deal with the energetics of α and β decays. You should know that a helium nucleus (two protons and two neutrons) is emitted in an α decay and that either an electron or a positron is emitted in a β decay. In each case, you should be able to find the resulting nucleus if the original nucleus is given. You should also be able to calculate the energy released in the decay if the various masses are given. Recall that the energy released in equal to the binding energy. If masses are given in atomic mass units, the conversion factor 931.5 MeV/u can be used. KNIG5491_02_ch30_pp991-1028.qxd 9/4/09 2:10 PM Page 1017 1017 Summary SUMMARY The goals of Chapter 30 have been to understand the physics of the nucleus and some of the applications of nuclear physics. GENERAL PRINCIPLES The Nucleus Nuclear Stability The nucleus is a small, dense, positive core at the center of an atom. Proton Z protons, charge +e, spin 12 N neutrons, charge 0, spin 12 Neutron The mass number is A=Z+N N Low-Z nuclei Line of stability move closer to the line of stability by beta decay. Most nuclei are not stable. Unstable nuclei undergo radioactive decay. Stable nuclei cluster along the line of stability in a plot of the isotopes. Alpha decay is energetically favorable for high-Z nuclei. Z Mechanisms by which unstable nuclei decay: Isotopes of an element have the same value of Z but different values of N. The strong force holds nuclei together: • It acts between any two nucleons. • It is short range. Adding neutrons to a nucleus allows the strong force to overcome the repulsive Coulomb force between protons. Decay Particle Penetration alpha beta-minus beta-plus gamma 4 low medium medium high He nucleus ee+ photon Alpha and beta decays change the nucleus; the daughter nucleus is a different element. The binding energy B of a nucleus depends on the mass difference between an atom and its constituents: Alpha decay: B = (Zm H + Nm n - m atom) * (931.49 MeV/u) A ZX : A-4 Z-2 Y Beta-minus decay: A ZX + a + energy : Z+1AY + b + energy IMPORTANT CONCEPTS Energy levels Energy Nucleons fill nuclear energy levels, similar to filling electron energy levels in atoms. Nucleons can often jump to lower energy levels by emitting beta particles or gamma photons. The quark model 12 C Neutrons Proton Nucleons (and other particles) are made of quarks. Quarks and leptons are fundamental particles. Protons d 2 u 1 2 3e Neutron d 1 3e u 1 2 2 3e Up quark d 2 1 3e 1 3e u 1 2 3e Down quark APPLICATIONS Radioactive decay N = N0 e-t/t 1 t/t1/2 N = N0 a b 2 Measuring radiation N The number of undecayed nuclei decreases exponentially with time t: The activity of a radioactive sample is the number of decays per second. Activity is related to the half-life as N0 0.50N0 0.37N0 The half-life R= 0.693N N = t t1/2 The radiation dose is measured in grays, where 0 0 t1/2 t1/2 = t ln 2 = 0.693t is the time in which half of any sample decays. t t 1 Gy = 1.00 J/kg of absorbed energy The relative biological effectiveness (RBE) is the biological effect of a dose relative to the biological effects of x rays. The dose equivalent is measured in sieverts, where dose equivalent in Sv = dose in Gy * RBE Some problems deal with the number and rate of decays. In an original collection of N0 nuclei, the number that remain undecayed at the end of time t is given by N = N0e-t/τ = N0(½) t/τ . The time constant τ is related to the half-life t1/2: t1/2 = τ ln2= 0.693τ. The activity is then given by R = R0e-t/τ = R0(½) t/τ where R0 is the activity at t = 0. Questions and Example Problems from Chapter 30 Question 1 For each nuclear energy-level diagram in the figure below, state whether it represents a nuclear ground state, an excited nuclear state, or an impossible nucleus Question 2 What kind of decay, if any, would you expect for the nuclei with the energy-level diagrams shown in the figure below? Problem 1 How many protons and how many neutrons are in (a) 3He, (b) 20Ne, (e) 60Co, and (d) 226Ra? Problem 2 Mercury 202 80 Hg has an atomic mass of 201.970617 u. Obtain the binding energy per nucleon (in MeV/nucleon). Problem 3 Calculate (in MeV) the binding energy per nucleon for 3He and 4He. Which is more tightly bound? Problem 4 Draw energy-level diagrams. similar to Figure 30.9, for all A = 10 nuclei listed in Appendix D. Show all the occupied neutron and proton levels. Which of these nuclei do you expect to be stable? 10 B is a stable nucleus, but 10Be and 10C are radioactive. 10Be undergoes beta-minus decay and 10 C undergoes beta-plus decay. In beta-minus decay, a neutron within the nucleus changes into a proton and an electron. In beta-plus decay, a proton changes into a neutron and a positron. Problem 5 For the following nuclei, each undergoing β- decay, write the decay process, identifying each daughter nucleus, with its chemical symbol and values for Z and A: (a) 146 C and (b) 212 82 Pb Problem 6 Determine the symbol ZA X for the parent nucleus whose α decay produces the same daughter as the β- decay of thallium 208 81 Tl . Problem 7 How many half-lives must elapse until (a) 90% and (b) 99% of a radioactive sample of atoms has decayed? Problem 8 The number of radioactive nuclei present at the start of an experiment is 4.60 × 1015. The number present twenty days later is 8.14 × 1014. What is the half-life (in days) of the nuclei?