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Nuclear Physics and Radioactivity

Nuclear Physics and Radioactivity. Chapter 30. Structure and Properties of the Nucleus. Nucleus – center of the atom Discovered by Rutherford Proton (+) charge: +1.6E-19 C Mass = 1.6726E-27 kg Neutron Discovered by James Chadwick (1932) Neutral (no charge) Mass = 1.6749E-27 kg

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Nuclear Physics and Radioactivity

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  1. Nuclear Physics and Radioactivity Chapter 30

  2. Structure and Properties of the Nucleus • Nucleus – center of the atom • Discovered by Rutherford • Proton • (+) charge: +1.6E-19 C • Mass = 1.6726E-27 kg • Neutron • Discovered by James Chadwick (1932) • Neutral (no charge) • Mass = 1.6749E-27 kg • Nucleons: protons and neutrons

  3. Structure and Properties of the Nucleus • Atomic number (A) • Number of protons • Determines the type of atom • For neutral atoms, the number of electrons is also equal to the atomic number • Mass number (Z) • Number of nucleons (protons and neutrons) • Number of neutrons = Z – A • Symbol • ZAX • 23892U

  4. Structure and Properties of the Nucleus • Isotopes • Same element with different numbers of neutrons • Same atomic number, but different mass numbers • Periodic table gives a weighted average of all the naturally occurring mass numbers (atomic mass) • Size of nucleus • Determined by Rutherford • Not an exact size due to wave-particle duality • r ≈ (1.2E-15m)(A1/3) • V = 4/3πr3 • V is proportional to A • However, we are not sure of the shape of the nucleus

  5. Example • Estimate the diameter of the following nuclei. • 11H • 4020Ca • 20882Pb • 23592U

  6. Structure and Properties of the Nucleus • Unified mass units (u) • Makes calculations easier • 126C: 12.000 000 u • Neutron = 1.008 665 u • Proton = 1.007 276 u • 11H: 1.007 825 u • Contains a proton and an electron • 1 u = 1.660 54E-27kg = 931.5 MeV/c2 • Nuclear spin quantum number, I • Both protons and neutrons are spin ½ • Whole integer if an even number of nucleons • Half integer if an odd number of nucleons

  7. Binding Energy • Total mass is always less than the mass of its parts • The missing mass is converted into energy • Binding energy = the total amount of energy required to break the nucleus into its protons and neutrons

  8. Example • Compare the mass of a 42He to the total mass of its constituent parts. What is the binding energy of the atom?

  9. Binding Energy • Binding energy per nucleon • Total binding energy of a nucleus divided by the number of nucleons (A) • 42He = 7.1 MeV • Drops as atoms get heavier • Easier to break apart nucleus • Allows for fission

  10. Example • Calculate the total binding energy and the binding energy per nucleon for 5626Fe, the most common stable isotope of iron.

  11. Example • What is the binding energy of the last neutron in 136C?

  12. Binding Energy • Nuclear forces • Strong nuclear force • Holds the protons together and electrically attracts neutral neutrons • Not a clear mathematical understanding yet • Works across a very short range ≈ 1/r7 • Stable nuclei have about the same number of neutrons and protons until the mass number gets to about 30 to 40; after that more neutrons are needed to counteract the increasing electrostatic repulsion of the protons • Weak nuclear force • Not clearly understood • Observed in some types of radioactive decay

  13. Radioactivity • Henri Becquerel (1896) • Studying phosphorescence • Uranium darkened a photographic plate without any external stimulus • Referred to as radioactivity • Marie (1867-1934) and Pierre (1859-1906) Curie • Isolated radium and polonium • Determined the radiation came from the nucleus

  14. Radioactivity • 3 types of radioactivity • Alpha rays (α) • Stopped by paper • Positively charged • Identified as a helium nucleus • Beta rays (β) • Stopped by a few mm of metal • Negatively charged • Electrons created by the nucleus (not part of the cloud) • Gamma rays (γ) • Passes through centimeters of lead • Electrically neutral • High energy photons (shorter wavelengths than x-rays)

  15. Alpha Decay • Parent nucleus • Original nucleus • Daughter nucleus • Nucleus of element after the decay • Different than parent nucleus • Transmutation: process of changing from one element to another • 22688Ra  22286Rn + 42He • 22688Ra: parent nucleus • 22286Rn: daughter nucleus • 42He: alpha particle

  16. Alpha Decay • Reason for alpha decay • Range of strong nuclear force is short • Acts only on close nucleons • Electrostatic force acts across the whole nucleus • For larger atoms, the nuclear force is unable to hold the atom together • Disintegration energy, or Q-value (Q) • Total energy released • Mass differences appears as KE of the recoiling daughter nucleus and the alpha particle • Mpc2 = MDc2 + mαc2 + Q • Q = KE • Q = Mpc2 – (MD + mα)c2 • If Q < 0, then the decay will not occur

  17. Example • Calculate the disintegration energy when 23292U (mass = 232.037 146 u) decays to 22890Th (228.028 731 u)with the emission of an alpha particle. (Assume the masses are for neutral atoms.)

  18. Alpha Decay • Why alpha particles? • Strongly bound • Mass is significantly less than four separate nucleons • Otherwise, it would violate the conservation of energy • Applications • Smoke detectors • Contains 24195Am • Radiation ionizes air molecules creating a current • Amount of radiation given off is too small to cause damage to humans

  19. Beta Decay • Transmutation occurs • 146C  147N + e- + neutrino • Conservation of nucleons • Conservation of charge • Neutron changes into a proton and a beta particle (electron) is created • e- = beta particle • NOT an orbital electron • Created within the nucleus • Function of the weak nuclear force • Neutrino • No charge • Small or zero mass

  20. Example • How much energy is released when 146C decays to 147N by beta emission?

  21. Beta Decay • Lost KE • Experiment showed that most beta particles did not have calculated KE • Momentum was also not conserved • Enrico Fermi (1901-1954) • Hypothesized particle: neutrino; “little neutral one” • Carries lost energy and momentum • No charge • Very small mass (<0.6 eV/c2) • Spin = ½(h/2π) • Symbol: ν (nu) • 146C  147N + e- + ν

  22. Beta Decay • Why beta decay? • Nucleus has too many neutrons vs. protons: unstable • Above line in graph • β+ decay? • Nucleus has too few neutrons vs. protons: unstable • Below line in graph • Emits a positron: positive charged electron • 1910Ne  199F + e+ + ν

  23. Beta Decay • Electron Capture • Nucleus absorbs one if its innermost electrons • Usually from the K shell (K capture) • Conservation of charge • Electron disappears • Proton becomes a neutron • 74Be + e- 73Li + ν

  24. Gamma Decay • High energy photons • Nucleus can be in an excited state • Gamma ray is emitted when a nucleus jumps to a lower state • Energy levels are much further apart (keV to MeV) • Higher states caused by collisions with other particles • * = excited state • X-ray vs. gamma ray • X-ray is used if the photon is produced by an electron-atom reaction • Gamma ray is used if the photon is produced in a nuclear process 125B β- (9.0 MeV) β- (13.4 MeV) 126C* γ (4.4 MeV) 126C

  25. Half Life and Rate of Decay • Radioactive decay • Not all of the atoms decay at the same time • Radioactive decay law • N = Noe-λt • N: number of remaining nuclei after time, t • No: initial number of nuclei at time, t = 0 • λ: decay constant; different for each isotope • Activity • Rate of decay • ΔN/Δt = λN • N = original number of nuclei • (ΔN/Δt) = (ΔN/Δt)oe-λt

  26. Half Life and Rate of Decay • Half life • Time it takes ½ of a given sample to decay • Carbon 14 • Half life = 5730 years • Used to determine the age of a once living object • T½ = 0.693/λ • T½ = half life (seconds) • λ = decay constant

  27. Example • The isotope 146C has a half-life of 5730 years. If at some time a sample contains 1E22 carbon-14 nuclei, what is the activity of the sample?

  28. Example • A laboratory has 1.49 μg of pure 137N, which has a half-life of 600 seconds. • How many nuclei are present initially? • What is the activity initially? • What is the activity after 1 hour? • After approximately how long will the activity drop to less than one per second (1 s-1)

  29. Decay Series • Decay series • Multiple decays of a parent isotope • Diagonal lines = alpha decays • Horizontal lines = beta decay • Explains why elements that should have disappeared from decay since the universe was formed are still around • Decay of heavier elements with longer half-life

  30. Radioactive Dating • Determines the age on an object • Living plants absorb CO2 • Small fraction is carbon-14 • n + 147N  146C + p+ • Nitrogen produces carbon • Plant is alive • Uses CO2 to build or replace tissue • Carbon-14 to carbon-12 ratio stays relatively constant • Plant dies • No new CO2 is brought into the plant • Carbon-14 decays into carbon-12 • The ratio of carbon-14 to carbon-12 decreases • Knowing the half-life of carbon-14 and the ratio of carbon-14 to carbon-12 allows us to estimate how long ago the plant died

  31. Example • The mass of carbon in an animal bone fragment found in an archeological site is 200 g. If the bone registers an activity of 16 decays/second, what is its age?

  32. Radioactive Dating • Limitations • After 60,000 years, the amount of carbon-14 drops below measureable amounts • Other isotopes can be used • Uranium-238 can measure the age of rocks to 4E9 (4 billion) years.

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