SPH4UI Physics Modern understanding: the ``onion picture Nuclear Binding, Radioactivity Nucleus Protons tom and neutrons Let s see what s inside! 3 Nice Try Introduction: Development of Nuclear Physics 1896 the birth of nuclear physics Becquerel discovered radioactivity in uranium compounds Rutherford showed the radiation had three types lpha (He nucleus) Beta (electrons) Gamma (high-energy photons) 1911 Rutherford, Geiger and Marsden performed scattering experiments Established the point mass nature of the nucleus Nuclear force was a new type of force 1919 Rutherford and coworkers first observed nuclear reactions in which naturally occurring alpha particles bombarded nitrogen nuclei to produce oxygen 1932 Cockcroft and Walton first used artificially accelerated protons to produce nuclear reactions 1932 Chadwick discovered the neutron 1933 the Curies discovered artificial radioactivity 1938 Hahn and Strassman discovered nuclear fission 1942 Fermi achieved the first controlled nuclear fission reactor 1
Some Properties of Nuclei ll nuclei are composed of protons and neutrons Exception is ordinary hydrogen with just a proton The atomic number (charge), Z, equals the number of protons in the nucleus The neutron number, N, is the number of neutrons in the nucleus The mass number,, is the number of nucleons in the nucleus = Z + N Nucleon is a generic term used to refer to either a proton or a neutron The mass number is not the same as the mass Notation Z X where X is the chemical symbol of the element 27 Example: l 13 Mass number is 27 tomic number is 13 Contains 13 protons Contains 14 (27 13) neutrons The Z may be omitted since the element can be used to determine Z Charge: Charge and mass The electron has a single negative charge, -e (e = 1.60217733 x 10-19 C) The proton has a single positive charge, +e Thus, charge of a nucleus is equal to Ze The neutron has no charge Makes it difficult to detect Mass: It is convenient to use atomic mass units, u, to express masses 1 u = 1.660559 x 10-27 kg Based on definition that the mass of one atom of C-12 is exactly 12 u Mass can also be expressed in MeV/c 2 From E R = m c 2 1 u = 931.494 MeV/c 2 Summary of Masses Masses Particle kg u MeV/c 2 Proton 1.6726 x 10-27 1.007276 938.28 Neutron 1.6750 x 10-27 1.008665 939.57 Electron 9.101 x 10-31 5.486x10-4 0.511 Quick problem: protons in your body What is the order of magnitude of the number of protons in your body? Of the number of neutrons? Of the number of electrons? Take your mass approximately equal to 70 kg. n iron nucleus (in hemoglobin) has a few more neutrons than protons, but in a typical water molecule there are eight neutrons and ten protons. So protons and neutrons are nearly equally numerous in your body, each contributing 35 kg out of a total body mass of 70 kg. N 1nucleon 1.67 10 kg 28 35kg 10 protons 27 Same amount of neutrons and electrons. 2
The Size of the Nucleus First investigated by Rutherford in scattering experiments He found an expression for how close an alpha particle moving toward the nucleus can come before being turned around by the Coulomb force The KE of the particle must be completely converted to PE 2 qq 2 1 2 e e eze 1 mv k k 2 r d or d 2 4k e Ze 2 For gold: d = 3.2 x 10-14 m, for silver: d = 2 x 10-14 m Such small lengths are often expressed in femtometers where 1 fm = 10-15 m (also called a fermi) mv Since the time of Rutherford, many other experiments have concluded the following Most nuclei are approximately spherical verage radius is Example: r r o r o = 1.2 x 10-15 m Z Size of Nucleus 1 3 27 l 13 has radius 15 r 3.610 m Density of Nuclei Nuclear Stability The volume of the nucleus (assumed to be spherical) is directly proportional to the total number of nucleons This suggests that all nuclei have nearly the same density Nucleons combine to form a nucleus as though they were tightly packed spheres There are very large repulsive electrostatic forces between protons These forces should cause the nucleus to fly apart The nuclei are stable because of the presence of another, shortrange force, called the nuclear (or strong) force This is an attractive force that acts between all nuclear particles The nuclear attractive force is stronger than the Coulomb repulsive force at the short ranges within the nucleus 3
BINDING ENERGY in MeV/nucleon 20/08/2010 Nuclear Stability chart Isotopes Light nuclei are most stable if N = Z Heavy nuclei are most stable when N > Z s the number of protons increase, the Coulomb force increases and so more nucleons are needed to keep the nucleus stable No nuclei are stable when Z > 83 The nuclei of all atoms of a particular element must contain the same number of protons They may contain varying numbers of neutrons Isotopes of an element have the same Z but differing N and values X Z atomic number (charge), Z neutron number, N nucleon number,, Example: 11 C 12 C 13 C 14 6 6 6 6 C The total energy of the bound system (the nucleus) is less than the combined energy of the separated nucleons This difference in energy is called the binding energy of the nucleus It can be thought of as the amount of energy you need to add to the nucleus to break it apart into separated protons and neutrons Binding Energy Binding Energy Plot Iron (Fe) is most binding energy/nucleon. Lighter have too few nucleons, heavier have too many. Fission Fission = Breaking large atoms into small Fusion = Combining small atoms into large Binding Energy per Nucleon 4
Binding Energy Notes Question Except for light nuclei, the binding energy is about 8 MeV per nucleon The curve peaks in the vicinity of = 60 Nuclei with mass numbers greater than or less than 60 are not as strongly bound as those near the middle of the periodic table The curve is slowly varying at > 40 This suggests that the nuclear force saturates particular nucleon can interact with only a limited number of other nucleons Where does the energy released in the nuclear reactions of the sun come from? (1) covalent bonds between atoms (2) binding energy of electrons to the nucleus (3) binding energy of nucleons Question Which element has the highest binding energy/nucleon? Question Neon (Z=10) Iron (Z=26) Iodine (Z=53) Which of the following is most correct for the total binding energy of an Iron atom (Z=26)? 9 MeV 234 MeV 270 MeV 504 Mev For Fe, B.E./nucleon 9MeV 56 26 Fe has 56 nucleons Total B.E 56x9=504 MeV 5
Binding Energy Einstein s famous equation E = m c 2 Big Problem: binding energy Proton: mc 2 = 938.3MeV Neutron: mc 2 = 939.5MeV dding these, get 1877.8MeV Calculate the average binding energy per nucleon of 93 41 Nb Using atomic mass units Deuteron: mc 2 =1875.6MeV Difference is Binding energy, 2.2MeV M Deuteron = M Proton + M Neutron Binding Energy Calculate the average binding energy per nucleon of 93 Nb 41 Radioactivity Given: m p = 1.007276u m n = 1.008665u 1u=931.5 MeV Find: E b =? In order to compute binding energy, let s first find the mass difference between the total mass of all protons and neutrons in Nb and subtract mass of the Nb: Number of protons: Number of neutrons: Mass difference: m 41m 52m m p n Nb Thus, binding energy is N 41 mc 2 0.842519u 931.5 MeV u Eb 8.44 MeV nucleon 93 p N 93 41 52 n u u u 41 1.007276 52 1.008665 92.9063768 0.8425192u 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 lpha particles The particles are 4 He nuclei Beta particles The particles are either electrons or positrons positron is the antiparticle of the electron Gamma rays It is similar to the electron except its charge is +e The rays are high energy photons 6
B field into screen Types of Radioactivity The Decay Processes General Rules Radioactive sources 4 a particles: He 2 nuclei b particles: electrons g detector photons (more energetic than x-rays) Barely penetrate a piece of paper Can penetrate a few mm of aluminum Can penetrate several cm of lead When one element changes into another element, the process is called spontaneous decay or transmutation The sum of the mass numbers,, 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 lpha Decay When a nucleus emits an alpha particle it loses two protons and two neutrons N decreases by 2 Z decreases by 2 decreases by 4 Symbolically Z X Y He 4 4 Z2 2 X is called the parent nucleus Y is called the daughter nucleus Decay of 226 Ra lpha Decay -- Example Ra Rn He 226 222 4 88 86 2 Half life for this decay is 1600 years Excess mass is converted into kinetic energy Momentum of the two particles is equal and opposite 7
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 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 Symbolically Z Z X Y e Z1 X Y e Z1 Beta Decay is the symbol for the neutrino is the symbol for the antineutrino To summarize, in beta decay, the following pairs of particles are emitted n electron and an antineutrino positron and a neutrino 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 B C * e 12 12 5 6 C* 12 12 6 6 Cg The C* indicates the Carbon nucleus is in an excited state Gamma emission doesn t change either or Z 8
Decay Rules Practice 1) Nucleon Number is conserved. 2) tomic Number (charge) is conserved. 3) Energy and momentum are conserved. a: example b: example g: example U Th a 238 234 92 90 P P g * 0 Z Z 0 recall 4 He a 2 1) 238 = 234 + 4 Nucleon number conserved 2) 92 = 90 + 2 Charge conserved n p e 1 1 0 0 1 1 0 0 Neutrino needed to conserve energy and momentum. nucleus undergoes a decay. Which of the following is FLSE? 1. Nucleon number decreases by 4 2. Neutron number decreases by 2 3. Charge on nucleus increases by 2 a decay is the emission of decreases by 4 Z decreases by 2 (charge decreases!) 4 He a 2 U Th He 238 234 4 Ex. 92 90 2 b Practice 234 The nucleus Th undergoes b 90 decay. Which of the following is true? 1. The number of protons in the daughter nucleus increases by one. 2. The number of neutrons in the daughter nucleus increases by one. decay is accompanied by the emission of an electron: creation of a charge -e. 234??? 234 0?? X e 0 90Th 91Pa e 1 1 0 0 0 0 In fact, n p e e inside the nucleus, and the electron and neutrino escape. Decay Which of the following decays is NOT allowed? 1 2 3 4 U Th a 238 234 92 90 Po Pb He 214 210 4 84 82 2 C Ng 14 14 6 7 K p e 40 40 0 0 19 20 1 0 238 = 234 + 4 92 = 90 + 2 214 = 210 + 4 84 = 82 + 2 14 = 14+0 6 <> 7+0 40 = 40+0+0 19 = 20-1+0 9
Decay The Decay Constant 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. 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 N R t N N t N Decays per second, or activity Start with 16 14 C atoms. Radioactivity N N t decay constant fter 6000 years, there are only 8 left. No. of nuclei present How many will be left after another 6000 years? 1) 0 2) 4 3) 8 Every 6000 years ½ of atoms decay The decay curve follows the equation N N e t 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 T 1 2 0 Decay Curve ln 2 0.693 10
Units Decay Function 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 1 N() t N e N 2 T1/2 t 0 0 t time Practice The half-life for beta-decay of 14 C is ~6,000 years. You test a fossil and find that only 25% of its 14 C is un-decayed. How old is the fossil? 3,000 years 6,000 years 12,000 years t 0 years: 100% remains t 6,000 years: 50% remains t 12,000 years: 25% remains Radioactivity Quantitatively Decays per second, or activity Survival: No. of nuclei present at time t decay constant N() t N e t 0 Instead of base e we can use base 1/2: t T1/2 1 2 Half life e t Then we can write N N t where T No. we started with at t=0 1/2 0.693 1 N() t N e N 2 T1/2 t 0 0 No. of nuclei present t 11
Radioactivity Example The half-life for beta-decay of 14 C is 5730 years. If you start with 1000 carbon-14 nuclei, how many will be around in 22920 years? 1 N() t N e N 2 N( t) T1/2 t 0 0 1 2 T1/2 N0 1 1000 2 62.5 t 22920 5730 t T 1/2 0.693 0.693 T1/2 0.693 5730 1.20910 N t N0e t 4 1.20910 4 22920) 1000e 62.5 Carbon Dating Uses of Radioactivity 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 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 Binding Energy Which system weighs more? 1) Two balls attached by a relaxed spring. 2) Two balls attached by a stretched spring. 3) They have the same weight. M 1 = M balls + M spring M 2 = M balls + M spring + E spring /c 2 M 2 M 1 = E spring /c 2 10-16 Kg 12
Strong Nuclear Force Q Values (nice to know) cts on Protons and Neutrons Strong enough to overcome Coulomb repulsion cts over very short distances Two atoms don t feel force Energy must also be conserved in nuclear reactions The energy required to balance a nuclear reaction is called the Q value of the reaction n exothermic reaction There is a mass loss in the reaction There is a release of energy Q is positive n 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 Problem: nuclear reactions Determine the product of the reaction What is the Q value of the reaction? Li He? n 7 4 X 1 3 2 Y 0 Determine the product of the reaction What is the Q value of the reaction? Li He n 7 4 3 2? Given: reaction Find: Q =? It is easier to use atomic mass units rather than kg. In order to balance the reaction, the total amount of nucleons (sum of -numbers) must be the same on both sides. Same for the Z-number. Number of nucleons (): 7 4 X 1 X 10 Number of protons (Z): 3 2 Y 0 Y 5 Thus, it is B, i.e. The Q-value is then 2 2 n 7 4 10 Li He B 7.016005u 4.002603u 10.012938u 1.008665u 931.5 Mev / u Q m c m m m m c 2.79MeV Li He B n 7 4 10 1 3 2 5 0 13
Summary Nuclear Reactions Nucleon number conserved Charge conserved Energy/Momentum conserved 4 a particles = He 2 nucleii b - particles = electrons g particles = high-energy photons N() t N0e t 0.693 Survival: T1/2 Decays Half-Life is time for ½ of atoms to decay 14