1. Nuclear Physics

2. The Future of Science “An eminent physicist has remarked that the future truths of Physical Science are to be looked for in the sixth place of decimals” – speech by Albert Michelson, 1894 (physicist who measured the speed of light) Why would a leading physicist say this? What changed this outlook? Would current physicists say this about physics today?

3. Nature of Science How does science advance? Do science theories (models) change? Is so when are they changed? Must science be experimentally verified to be accepted? How do scientists empirically verify what they cannot see?

4. Isotopic Notation El = element symbol (note lower case second letter) A = atomic mass = sum of neutrons and protons = mass of isotope Z = atomic number = number of protons = identity of element Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

5. Parts of an Atom Subatomic Particle Relative Mass Relative Charge Location electronzero clouds outside nucleus protonone amu (u) +1inside nucleus neutronone amu (u) neutralinside nucleus

6. Nuclear Definitions Nuclide – nucleus with a specific number of protons and neutrons Nucleons – constituents of the nucleus (number of protons and neutrons) Unified Atomic Mass Unit (u) – 1/12 of the mass of an atom of carbon

7. Isotopes The same element (same number of protons) can have different isotopes because atoms can have differing numbers of neutrons.  Chemical properties of different isotopes of the same element remain the same.  Nuclear properties depend on the stability of the nucleus. Isotopes

8. The Mass Spectrometer The existence of isotopes is demonstrated by a mass spectrometer. In a mass spectrometer ionized ions of an element are emitted through a pair of slits (S 1 ) that align the beam. This beam enters a region of electric and magnetic fields approaching a second slit (S 2 ) that allows ions of a given velocity to pass. A second magnetic field bends these ions into a circular paths according to their mass. Radius of the circular path is If isotopes are present, the heavier atoms follow a longer path. Measuring the radius allows the mass to be calculated. Physics for the IB Diploma 5th Edition (Tsokos) 2008

9. Strong Nuclear Force From Coulomb’s Law we know that 2 positive charged particles repel each other, why then does a nucleus with 2 or more protons not fly apart? a.The gravitational attraction holds them together. b.Coulomb’s Law doesn’t apply to protons in a nucleus c.There is a stronger attractive force that binds the nucleus together. Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

10. Strong Nuclear Force Force that holds the nucleus together A fundamental force Almost independent of electric charge –For the same distance, nearly the same force exists between 2 protons, 2 neutrons, and a proton and neutron. Short range force (10 -15 m) Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed. Strong Force Nuclear Forces

11. Stability of the Nucleus For stability the electrostatic repulsion of the protons must be balanced by the attraction of the nucleons due to the strong nuclear force. –A proton electrostatically repels all other protons in a nucleus. –A proton or neutron only attracts its nearest neighbor by the strong nuclear force. –As the number of protons increase a greater number of neutrons are required to balance the electrostatic repulsion.

12. Stable Nuclei  Small atoms having a 1:1 proton to neutron ratio are stable. ex. Most carbon atoms are carbon-12 isotopes. About one percent are carbon-13 and a few are radioactive carbon-14.  14C has _____ protons and _____ neutrons. Because it has too many neutrons, the nucleus will give off a radioactive particle and change into nitrogen-14.  Larger nuclei need more neutrons to remain stable.

13. Binding Energy & Mass Defect Binding Energy The amount of energy required to break a nucleus apart Mass Defect The difference in mass between the sum of the individual protons and neutrons masses and the mass of the stable nuclei. Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed. Binding energy = (Mass defect)c 2

14. Electron Volt (eV) Unit of work (or energy) much smaller than the Joule. If 1 electron moves through a potential difference of 1V then 1eV of work is done. W = Vq and 1eV is the work done moving one electron through a potential difference of 1 V. Therefore, 1eV = 1.6×10 -19 J

15. Binding Energy Calculate the binding energy of a Helium Nucleus Calculating in MeV, since c is a constant it can be shown that when ∆m= 1u  1u = 931.5 MeV Binding energy = (Δm)c 2 1u=1.6605 x 10 -27 kg http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

16. Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed. Binding Energy

17. Main features Binding energy per nucleon for Hydrogen is 0 Curve rises steeply for low values of A Peaks at nuclei He-4, C-12, and O-16 (more stable compared to neighbors) The maximum curve value is at A=62 ) (very stable) Curve drops gently from peak at A=62 Most nuclei have a binding energy between 7 and 9 MeV Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed. Binding Energy

18. Stable Isotopes (Nuclei) The largest stable nuclei is Bismuth ( ) above that all nuclei are unstable and will spontaneously break apart. Any nuclei that is to the right or left of the blue curve is considered unstable. Unstable nuclei decay or change into other nuclei that are closer to the stable nuclei. This decay is known as _____________. Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed. After ___ protons a stable nucleus will have more neutrons than protons. 20

19. Discovery of Radioactivity Was Becquerel’s discovery based on luck? Explain What allowed Becquerel to explain the exposed photographic plate? Was Becquerel’s observation with no a priori (preconceptions)? What lessons about science can be ascertained from this historical vignette? http://www.whodiscoveredit.com/wp-content/uploads/2010/03/Radioactivity-Henri- Becquerel-.jpg

20. Three Types of Nuclear Radiation Alpha Beta Gamma

21. Three Types of Nuclear Radiation Alpha Beta Gamma Existence confirmed by letting all three radiations pass through a magnetic field. Showed two were oppositely charged, one was neutral. Copyright ©2007 Pearson Prentice Hall, Inc.

22. Alpha Particle Alpha (  ) – Lowest energy, i.e. Least penetrating power Largest ionization power (greatest mass) Unstable nucleus may emit a helium nucleus consisting of 2 protons and 2 neutrons. Specific energies - evidence of nuclear energy levels

23. Alpha Reaction http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

24. Beta Particle Beta (  )  Second most penetrating power and ionization power  Involves the transformation of a neutron to a proton (β - decay) or a proton to a neutron (β + decay)  Caused by the weak nuclear force  Involves the release of a neutrino (β + decay) or antineutrino (β - decay)  particle that carries away energy  zero electrical charge and very weak interaction with matter.  Continuous range of energies.

25. β - Decay When there are too many neutrons in a nucleus, one of them will change into a proton.  The nucleus emits a high speed electron - e β - particle and an antineutrino ( ) Parent Nucleus Daughter Nucleus β - Particle (electron) Antineutrino

26. Beta Decay http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

27. β - Decay http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

28. β + Decay Nucleus emits a positron and a neutrino A positron (β + particle) has the same mass as an electron but a positive charge (+e) –Created when a proton changes to a neutron. A neutrino is a particle that carries away energy from a β decay Parent Nucleus Daughter Nucleus β + Particle (Positron) Neutrino

29. Gamma Radiation Gamma Radiation (  )  Most penetrating (greatest energy)  Lowest ionization power (no mass)  Not a particle - pure energy  Accompanies most other emissions  Allows nucleus to give off excess energy from nuclear rearrangement.  Discrete energy values – evidence of nuclear energy levels

30. Relative Penetrating Power Alpha (  ), beta (  ) and gamma (  )radiation A gamma ray whose lead half thickness is 1 cm (0.4 inches) of lead would require 6 cm (2½ inches) of concrete or 9 cm (3½ inches) of packed dirt to reduce its intensity by the same amount.leadconcrete Source: http://en.wikipedia.org/wiki/Gamma_ray http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

31. Relative Ionization Power Source: https://en.wikipedia.org/wiki/Ionizing_radiation Ionization Power – the ability to remove electrons from atoms creating positive ions Alpha particle – Very high ionization power. largest mass and charge Beta particle – Moderate ionization power smaller mass and charge Gamma particle – Weak ionization power virtually no mass.

32. Decay Reactions Uranium - 238 changes to an atom of thorium - 234 Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

33. Decay Reactions Thorium-234 beta decays to Protactinium-234 Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

34. Decay Reactions Bismuth - 210 emits a beta particle and gamma radiation

35. Nuclear Radiation Summary RayReaction Symbol Relative Mass Electrical Charge Penetrating Power alpha  4 amu (u)+2stopped by paper beta  1/1837 ustopped by Al foil gamma  00Lead, thick concrete Radioactivity

36. Decay of U-238 Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

37. Half Life How often does an atom emit radiation? It is not possible to predict exactly when a particular atom will undergo radioactive decay. It is possible to know how much of a sample will decay in a certain time if you know the…. Half Life NOS What other discipline does the concept of half-life draw upon? What does the statement statistics show ‘correlation not causality’ mean? Does science show correlation, causality, or both? Explain

38. Half Life HALF LIFE (t 1/2 ) - The amount of time required for half the radioactive isotopes in a sample to emit radiation (aka – undergo decay, aka – transmutate into another element) Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

39. Half-Life Calculations Sample #1: The half life of radioisotope “Q” is three days. If a sample of Q has a mass of 20 mg, what mass of Q remains after 12 days?

40. the probability of decay per unit time. The greater the decay constant. The more rapid the material decays. Example: 1.What is the probability that a radioactive nucleus will decay during a time interval equal to its half-life? 2.What is the probability that it will have decayed after the passage of three half-lives. 3.A nucleus has remained undecayed after the passage of four half-lives. What is the probability it will decay during the next half-life. Decay Constant ( λ) 0.5 0.875

41. Decay Equation Where –N = number of radioactive nuclei present –N o = original number of radioactive nuclei –t = time –λ = decay constant –T 1/2 = half-life

42. Decay Equation Half-life derivation from the decay equation From the definition of a half-life, when t = T ½ then N = N 0 /2  simplifying, Taking the natural log  Solving for the decay constant Another form of the half-life equation is

43. Half-Life Calculations Sample #2: A sample of a rare radioisotope has been found to have a mass of 150 mg. After 65 minutes the mass of the radioisotope has been reduced to 37.5 mg. What is the half life of the isotope?

44. Half-Life Calculations The Chernobyl nuclear reactor accident in the Soviet Union in 1986 released a large plume of radioactive isotopes into the atmosphere. Of particular health concern was the short- lived (half life: 8.0 days) isotope 131 I, which, when ingested, is concentrated in and damages the thyroid gland. This isotope was deposited on plants that were eaten by cows, which then gave milk with dangerous levels of 131 I. This milk couldn’t be used for drinking, but it could be used to make cheese, which can be stored until radiation levels have decreased. How long would a sample of cheese need to be stored until the number of radioactive atoms decreased to 3% of the initial value?

45. Activity Number of disintegrations per second that occurs in a radioactive sample Where ΔN = change in number of nuclei N = number of radioactive nuclei λ = decay constant SI Unit: becquerel (Bq) 1 Bq=1 disintegration/second Curie (Ci) = activity of one gram of pure radium. 1 Ci = 3.70 x 10 10 Bq

46. Activity Another form for activity is (calculus) Taking the derivative (more calculus) where Substituting, Where A 0 = initial activity λ = decay constant

47. Activity Half life – interval of time after which the activity of a radioactive sample is reduced by a factor of 2. Calculating Half-life from an Activity curve Note the original activity (A 0 ) On the curve find the point where A = A 0 /2 The time of this point is the half life.

48. Half-Life ElementIsotopeHalf-LifeRadiation Emitted Hydrogen 3H3H12.3 yearsbeta Carbon 14 C5730 yearsbeta Iodine 131 I80.7 daysBeta Lead 212 Pb10.6 hoursBeta Polonium 194 Po0.7 secondsAlpha Polonium 210 Po138 daysAlpha Uranium 227 U1.1 minutesAlpha Uranium 235 U7.1 x 10 8 yearsAlpha Uranium 238 U4.51 x 10 9 yearsAlpha Plutonium 236 Pu2.85 yearsAlpha Plutonium 242 Pu3.79 x 10 5 yearsAlpha

49. Geiger Counter Detect ionization caused by radioactive particles. Gas filled metal cannister Thin window on one end allows α,β, or γ particle to enter gas filled cylinder. Particle collides with and ionizes gas molecule. Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

50. Geiger Counter The electron produced by this is attracted to a positive wire. Other molecules are ionized as it moves toward wire. All of these electrons flow to the wire and cause a pulse that can be counted or produce a click. The number of clicks correspond to the number of disintegrations. Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed. Geiger Tube

51. Cathode Ray Tube A vacuum in a glass bottle, with a heating element on one end and a phosphor coated screen on the other Electrons are released at the cathode (negative terminal) and are attracted to the anode (positive terminal) A beam of electrons is produced These electrons strike the phosphor coated screen causing a flash of light. Technology used in TVs and computer monitors http://www.physics.fsu.edu/users/ng/Courses/phy2054c/Labs/Expt05/e05-f2.gif Note: The terms anode and cathode are reversed in a cathode tube from their definitions in a battery.

52. Historical Developments JJ Thomson discovered he could deflect these cathode rays in an electric field. The rays moved toward the positive plate indicating that they were negatively charged. New experiment arranged coils of wire to produce a magnetic field perpendicular to the electric field. By adjusting the strengths of the fields the rays could be deflected, in one direction by the electric field, and back an equal amount by the magnetic field. The forces were balanced. http:// webs.mn.catholic.edu.au/physics/emery/assets/hsc_id12.gif

53. http://www-outreach.phy.cam.ac.uk/camphy/electron/electron5_1.htm Historical Developments Setting the forces of the electric field and magnetic field equal to each other, Thomson was able to calculate the speed of the charge. Recall, F electric =Eq and F magnetic =qvB Next, he calculated the specific charge (charge/mass) Turning off the magnetic field, the deflection of the ray by just the electric field could be measured. v=E/B Experiment

54. Discovery of the Electron In 1897, J.J. Thomson had found a negative charged particle that had a specific charge two thousand times greater than that of the hydrogen ion. (smallest ion measured at that time) He concluded that the particles, which he called 'corpuscles', were a universal constituent of matter - they form part of all the atoms in the universe. Today we call these electrons Source: http://www-outreach.phy.cam.ac.uk/camphy/electron

55. Dali – Science, Religion, & Art Corpuscular Madonna, 1952 Assumpta Corpuscularia Lapislazulina, 1952

56. Historical Development 1906 JJ Thomson proposed a ‘plum pudding’ model of the atom. A positive sphere contained embedded negative charge particles (electrons) Dalton Model Pudding Model NOS Why was it proposed? What did the plum pudding model explain? What did it not explain? What does this show about scientific theories (models)?

57. Historical Development The Rutherford Model of the Atom In 1911 Rutherford proposed the nuclear model of atomic structure. An atom consists of a central nucleus (where most of the mass of the atom is concentrated) having a positive charge, surrounded by moving electrons carrying negative charge. http://physics.bgsu.edu/~stoner/P202/atoms/img006.JPG Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed. Rutherford

58. Particle Scattering Experiment Geiger and Marsden confirmed Rutherford’s nucleus model through the following experiment. –Detector a ZnS screen observed with a microscope –Measured the number of particles deflected at various angles Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

59. Particle Scattering Experiment Findings: Most particles passed through with no deflection. A few particles deflected –Indicates contact with nucleus -Some backscattering implied atom’s mass concentrated in a small nucleus -Scattering angle consistent with Coulomb’s law for a positive charge repelling the α particle Estimated the size of the nucleus (»10 -14 m) and the size of the atom (»10 -10 m). Most of the space occupied by the atom is empty space Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

60. Derivation of Radius of Nucleus the closest approach to a nucleus, r min, occurs when the particle’s initial direction is along the line joining the centers of particle and nucleus. at the point of closest approach, the speed of the particle is zero. K.E. Lost = E.P.E. gained Electrical potential at a distance r from a point charge Q is given by For a nucleus of atomic number Z, the charge is Ze, where e is the magnitude of the charge on one proton. The alpha particle’s charge is 2e Therefore, the energy, EPE, of an alpha particle placed at distance, r min, from a charge Ze is given by So, Derivation source: http://www.saburchill.com/physics/chapters Atom History http://www.saburchill.com/physics/chapters

61. Millikan’s Oil Drop Experiment Small drops of oil were allowed to fall into a region between two metal plates, (the top plate had a hole in it). The drops were ionized by friction or by a beam of x-rays. The terminal speed of a drop as it fell through the air, with V = 0, was measured with the radius of the drop ( mass) calculated from this. A voltage, V, was applied to the plates resulting in a new terminal speed of the same drop. The change in the terminal speed of the drop was used to calculate the magnitude of the charge on the drop. http://cwx.prenhall.com/bookbind/pubbooks/hillche m3/medialib/media_portfolio/text_images/CH07/F G07_04.JPG http://www.britannica.com/nobel/cap/omillik001a4.html Oil Drop

62. Millikan’s Oil Drop Experiment Findings: All the charges were found to be integral multiples of a basic unit of charge, assumed to be the charge on one electron. The value, e, is approximately -1.6×10 -19 C. Derivation: A drop having a charge q and mass m. If the drop is stationary, then the two forces acting on it are equal. where E is the field strength. Recall, E=V/d where d is the distance between the plates http://cwx.prenhall.com/bookbind/pubbooks/hillche m3/medialib/media_portfolio/text_images/CH07/F G07_04.JPG http://www.britannica.com/nobel/cap/omillik001a4.html Eq=mg In practice, it is still necessary to make a measurement of the terminal speed of the drop in order to find its radius and hence its mass Derivation source: http://www.saburchill.com/physics/chapters

63. Discovery of the Proton The magnetic field prevented β particles from reaching the detector. With no gas in the container, flashes of light were seen on the screen at a rate proportional to the intensity of the source of radiation. When the container was filled with nitrogen gas, the flashes became more frequent. Rutherford suggested that as a particle knocks a proton out of a nitrogen nucleus. These fast moving protons then hit the screen causing the flash of light. http://www.saburchill.com/physics/chapters

64. Discovery of the Proton  Proton Early example  artificial transmutation of an element (the changing of one element into another). The mass of the proton was measured by deflection in a magnetic field. Classic Experiment  the discovery of the proton. http://www.saburchill.com/physics/chapters

65. Discovery of the Neutron Chadwick (in 1932) Alpha particles from the polonium hit the beryllium and caused it to emit a very penetrating radiation. The "penetrating power" was measured by finding the thickness of metal needed to absorb the radiation. When the radiation hit paraffin wax (or any other substance containing hydrogen), protons were emitted. http://www.saburchill.com/physics/chapters

66. Discovery of the Neutron The maximum energy of the protons was estimated using the absorber sheets and found to correspond to a speed, u = 3.3×10 7 ms -1. Chadwick proposed the following reaction:  neutron when the radiation collided with nitrogen atoms they moved with a maximum speed of V = 4.7×10 6 ms -1. http://www.saburchill.com/physics/chapters

67. Discovery of the Neutron When a particle of mass m moving at speed u has a "head-on" elastic collision with a stationary particle of mass M, it can be shown that the particle of mass M has a speed V, after the collision, given by. collision between neutrons and protons collision between neutrons and nitrogen nuclei Therefore, the mass of a neutron, m » 1.15 times the mass of a proton http://www.saburchill.com/physics/chapters

68. Atomic Spectra All objects emit electromagnetic waves. For a solid object, such as the hot filament of a light bulb, these waves have a continuous range of wavelengths. The continuous range of wavelengths is a result of the entire collection of atoms that make up the solid. http://www.fotosearch.com/bthumb/DGV/DGV049/ST002346.jpg http://pennymaxwell.files.wordpress.com/2008/10/light-bulb-glowing-filament-ahd.jpg

69. Atomic Spectra Individual atoms, free of the strong interactions that are present in a solid, emit only certain specific wavelengths that are unique to those atoms. http://www.ivstandards.com/tech/samprep/images/samprep.gif

70. Atomic Spectra Under normal conditions electrons occupy the lowest energy level (ground level) If an excited atom absorbs energy the electron leaves the ground state and occupy a higher energy level. The electron then transitions back down to a lower energy state. –This energy is released as a photon. –This photon’s energy is equal to the difference in energy of the energy levels. –Since wavelength can be directly related to energy, the photons have well defined wavelengths that are specific to the atom. Wilson,Buffa, College Physics, 4 th ed 2000 Prentice Hall Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed. Copywrited by Holt, Rinehart, & Winston

71. Atomic Spectra Emission spectra can be observed by supplying a sufficiently large potential difference across the gas within a tube. Individual wavelengths emitted by the gas can be observed. Emission Spectrum Copyright ©2007 Pearson Prentice Hall, Inc.

72. Atomic Spectra An applied voltage excites the atoms of the gas. These excited electrons transition to higher energy levels. The excited electrons transition back down to lower energy levels releasing photons of specific wavelengths. These wavelengths show up as the emission spectrum of the element. Emission Spectrum Copyright ©2007 Pearson Prentice Hall, Inc.

73. Atomic Spectra To study the behaviour of individual atoms, low-pressure gases are used in which the atoms are relatively far apart. A source of radiation that contains all wavelengths is passed through the sample of gas and the resultant spectrum is examined. The gas absorbs some of the wavelengths of the light source. The observed spectrum, therefore, has lines missing which correspond to the absorbed wavelengths. Absorption Spectrum

74. Atomic Spectra If wavelengths of light do not correspond to any of the photon wavelengths released by the electron transitioning down, the light passes through without absorption. However, if the wavelength corresponds to a wavelength given off by a transition, the electron will absorb this light exciting the electron to a higher energy level. When this excited electron transitions back to the ground state, the photon given off scatters not reaching the screen producing a missing line. These missing lines correspond to the emission spectrum Absorption Spectrum Copyright ©2007 Pearson Prentice Hall, Inc.

75. Emission and Absorption of Photons Copyright ©2007 Pearson Prentice Hall, Inc.

76. Emission Spectra of Hydrogen From 1860-1865 spectroscopy developed. Anders Angstrom accurately measured the first four visible lines of hydrogen. By trial and error a Swiss school teacher, Johann Balmer, found a formula in 1885 which correctly predicted the wavelengths of Angstrom’s four visible lines. Balmer’s formula was Where C 2 = 3645.6 x 10 8 cm and is known as the convergence limit. These four lines became know as the Balmer Series

77. Emission Spectra of Hydrogen By the time Balmer finished his empirical formula equation, ten more lines in the violet and ultraviolet range had been measured. These newly measured lines agreed to the empirical formula to within 0.1%! Encouraged by his success, Balmer speculated that other hydrogen series might exist of the form: Balmer was correct.

78. Emission Spectra of Hydrogen In 1888 Johannes Rydberg, a Swedish physicist, combines all of Balmer series into a single formula of the form: –Where n f and n i are integers. –n i = n f + 1 –The Rydberg constant (R) = 1.0973 x 10 7 m -1 Atomic Spectra

79. ‘Solar System’ Atomic Model Typical depiction of the atom even today on some science books –Model I remember from high school. Is this the current scientific model? Limitations to the model How would you explain to a younger sibling or student that their science book has an inaccurate picture on the cover? Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed. NOS

80. Rutherford Model of the Atom 1911 ‘“solar system” model of the atom – electrons orbiting a small, positively charged nucleus. Limitations of Rutherford’s Model Only accounts for half of the nuclear mass. –Rutherford speculated that the difference between the mass of the protons and the mass of the nucleus could be accounted for by groupings of neutral particles, each consisting of a bound electron-proton pair. –Discovery of the neutron (1932) explained this. Copyright ©2007 Pearson Prentice Hall, Inc.

81. Rutherford Model of the Atom Limitations of Rutherford’s Model What keeps the protons confined in such a small space –Rutherford thought that “The nucleus although of minute dimensions, is in itself a very complex system consisting of positively and negatively charged bodies bound closely by intense electrical forces.” –1921 recognized that the electrostatic force did not hold the nucleus together and there had to be another force that did – strong nuclear force. Copywrited by Holt, Rinehart, & Winston

82. Rutherford Model of the Atom Limitations of Rutherford’s Model How do electrons orbit around the nucleus to form a stable atom and how does this movement account for observed spectral patterns. With Rutherford’s model – theory of electromagnetism required that an accelerated charge should radiate electromagnetic waves and lose energy. –Electron moves in a circular path – centripetal acceleration. –Loss of energy cause the electron to fall out of orbit and spiral into the nucleus.

83. Rutherford Model of the Atom Limitations of Rutherford’s Model How do electrons orbit around the nucleus to form a stable atom and how does this movement account for observed spectral patterns. With Rutherford’s model – The frequency of radiation emitted by a continuously radiating electron would have a continuous spectrum, rather than the individual frequencies that are actually observed. Experimental results from Atomic spectra of atoms showed specific frequencies associated with each type of atom.

84. The Bohr Model 1913 Neils Bohr proposed a new model with the following postulates that addressed the weaknesses of Rutherford’s model. Postulate 1 - The electron moves in a circular orbit around the nucleus under the influence of the electrostatic force. Bohr Model

85. The Bohr Model Postulate 2 - Only certain orbits are stable. –These are the orbits in which the electron does not radiate. –Energy is fixed and stationary. –Classical mechanics may be used to describe the electron’s motion in these stable orbits.

86. The Bohr Model Postulate 3 - Radiation is emitted or absorbed if an electron moves between energy levels. –Radiation is released in the form of a photon. –The frequency of the photon emitted is related to the difference in the energy levels according to the Planck-Einstein formula: Wilson,Buffa, College Physics, 4 th ed 2000 Prentice Hall

87. The Bohr Model Postulate 4 - The size of the stable orbits are determined by imposing a further quantum constraint on the angular momentum of the electrons. n = 1, 2, 3 ….

88. The Bohr Model Derivation of the energy of allowed levels. Total Energy – kinetic energy and potential energy The electrostatic force on the electron is This electrostatic force provides the centripetal force.  substituting Z=atomic number e= elementary charge

89. The Bohr Model Derivation of the energy of allowed levels – cont. To determine the radius, Bohr assumed that the angular momentum of an electron is quantized. Solving for v,substituting into  solving for r Substituting back into the energy expression substituting values in for h, m, k and e n = 1, 2, 3 ….

90. Bohr Energy Levels Converting to eV Energy Level Diagrams – visual representation of the energy levels produced by the previous equation. ground state – lowest energy level (n = 1) excited states – higher energy levels (n > 1) Ionization energy – energy needed to remove an electron. –Energy required to raise electron from ground state (n = 1) to highest possible state (n = ∞) –For hydrogen 13.6 eV is required n = 1, 2, 3 …. Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

91. Bohr’s Model of the Hydrogen Atom Assuming that the radiation emitted from excited atoms corresponds to the energy difference between two levels: with the known values of h, m, k, e, and c the first term equals 1.097 x 10 7 m -1 or Rydberg’s constant R or the empirical Rydberg’s Equation Bohr regarded this proof the crowning achievement of his quantum theory of hydrogen. n i, n f = 1, 2, 3 …. and n i < n f

92. Bohr’s Model of the Hydrogen Atom Bohr’s model only partially explained the emission spectrum lines of hydrogen Wilson,Buffa, College Physics, 4 th ed 2000 Prentice Hall Copywrited by Holt, Rinehart, & Winston

93. Bohr’s Model Limitations Only treat one-electron atoms (hydrogen atom) Treats circular orbits only. Does not predict the intensities of different spectral lines. Inconsistent with the uncertainty principle. Does not predict the splittings of energy levels due to the interaction of the magnetic field of the proton and the electron’s angular momentum and spin. Wilson,Buffa, College Physics, 4 th ed 2000 Prentice Hall

94. de Broglie Waves and the Bohr Model Bohr’s assumption that the angular momentum of the electron is a quantized number was explained by de Broglie de Broglie proposed that the allowed orbits were those which comprised an integral number of wavelengths of the electron – a kind of standing wave. Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed. Copyright ©2007 Pearson Prentice Hall, Inc.

95. de Broglie Waves and the Bohr Model de Broglie showed the electron in Bohr’s circular orbit as a standing particle wave. For a standing wave an integer number of wavelength must be present. For the circular orbit the total distance in the circumference then Calculating momentum and finally linear momentum n = 1, 2, 3 …. This agrees with Bohr’s assumption for the quantization of angular momentum of an electron Wilson,Buffa, College Physics, 4 th ed 2000 Prentice Hall

96. Schrödinger Theory 1926 Erwin Schrödinger proposed a quantum model for the behavior of electrons in atoms. Schrödinger theory assumed that there is a wave associated with the electron. The wave is a function of position x and time t and called the wavefunction, ψ(x,t) Given the forces acting an electron, it is possible to solve a complicated differential equation obeyed by the wavefunction and obtain ψ(x,t)

97. Schrödinger Theory Wavefunction (ψ) Properties Source: http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

98. Schrödinger Theory Max Born, a German scientist, showed what ψ(x,t) really meant. He proposed that |ψ(x,t)| 2 (the square of the absolute value of the wavefunction) represents the probability that an electron will be found near position x at time t So Schrödinger theory gives the probability for finding an electron somewhere. Radically different from classic physics as it does not pinpoint an electron at a particular point in space. When the theory is applied to the electron in a hydrogen atom it results in Same as derived by Bohr http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html

99. Schrödinger Theory predicts that the electron in the hydrogen atom has quantized energy. The electron can be found in one of the energy levels of the atom. If the electron is in a high energy level, the electron can transition to a lower level by emitting a photon of energy equal to the difference in energy between the levels of the transition. Predicts the probability that a particular transition will occur. Explains atomic spectra Physics for the IB Diploma 5th Edition (Tsokos) 2008 Schrodinger

100. Schrödinger Theory The variation of the probability distribution of an electron with distance r from the nucleus for the lowest energy level shown. The height is proportional to |ψ(x,t)| 2 The shaded area is the probability for finding the electron at a distance from the nucleus between r = a and r = b. This probability can be represented as an electron cloud model of the atom shown below. Physics for the IB Diploma 5th Edition (Tsokos) 2008 Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

101. Schrödinger Atomic Model Electron ‘Cloud’ model – shows probability of the location of electron by placing a dot everywhere the electron is found. –Dense regions show the highest probability locations of the electron. –Less dense regions show lower probability locations. Modern Model Wilson,Buffa, College Physics, 4 th ed 2000 Prentice Hall

102. Atomic Transitions An electron in the state n = 3 can return to the ground level through three transitions. So three different photon frequencies will be observed in the emission spectrum of hydrogen from this level Physics for the IB Diploma 5th Edition (Tsokos) 2008

103. Atomic Transitions Example Problem If electrons are excited to the n = 4 state, how many different photon frequencies will be observed in the emission spectrum of hydrogen? 6 Physics for the IB Diploma 5th Edition (Tsokos) 2008

104. Atomic Transitions Example Problem What is the wavelength of the photon emitted when a hydrogen atom makes a transition from n=3 to n=1? Physics for the IB Diploma 5th Edition (Tsokos) 2008 R = 1.097 x 10 7 m -1

105. Atomic Transitions Example Problem Which transition corresponds to photons of larger wavelength, n=5 to n=3 or n=6 to n=4? Physics for the IB Diploma 5th Edition (Tsokos) 2008 Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed. Wilson,Buffa, College Physics, 4 th ed 2000 Prentice Hall

106. Nuclear Energy Levels The nucleus exists in discrete energy levels as well. Evidenced by alpha and gamma decay as the nuclei emits –alpha particles with energies that are discrete. –gamma ray photons with energies that are discrete The magnesium atom shown undergoes a gamma decay. What is the energy of the released photon? Physics for the IB Diploma 5th Edition (Tsokos) 2008

107. Nuclear Energy Levels The figure shows energy levels for plutonium and uranium undergoing alpha decay. What is the energy of the released alpha particles? Physics for the IB Diploma 5th Edition (Tsokos) 2008

108. Nuclear Energy Levels Beta decays does not evidence nuclear energy levels as the electron has a continuous range of energies. The figure of beta decay of bismuth shows an energy released with the beta decay of 0.57 MeV. This energy is shared between the electron, the antineutrino, and the polonium nucleus. So the electron does not always have the maximum energy of 0.57 MeV. Depending on the angles between the particles, the electron can have an energy anywhere from zero up to the maximum value. (continuous range) Physics for the IB Diploma 5th Edition (Tsokos) 2008

109. Nuclear Power Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

110. Nuclear Fission Splitting of a massive nucleus into two less massive fragments. Discovered in 1939 by 4 German scientists Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

111. Nuclear Fission of Uranium A slow moving neutron (thermal neutron) collides with and is absorbed by the Uranium nucleus. –Thermal neutron (slower) more likely produce fission in U-235 –High energy neutron (fast) more likely produce neutron capture in U- 238 (more abundant than U-235) Nucleus begins to vibrate until the strong nuclear force can no longer keep it together and it breaks apart releasing energy. This breaking up releases large amounts of energy. –Energy released is primarily as K.E. of the fragments. –Energy source was E.P.E. of the nucleus. – 200 MeV per fission –~10 8 greater than normal chemical reactions

112. Nuclear Fission of Uranium 2 naturally occurring isotopes U-238 (99.275%) and U-235 (0.720%). –U-235 much higher probability of fission Primary nuclear fuel Uranium enriched to increase the percentage of U-235 Uranium fissions on average produce 2.5 neutrons.

113. Chain Reaction Occurs when each neutron produced in a fission reaction produces other fission reactions causing a rapid multiplication of fissions and energy. An uncontrolled reaction of this type  Atomic Bomb Controlled reaction  Nuclear Power Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

114. Copywrited by Holt, Rinehart, & Winston Fission

115. Fuel Elements – contains the fissionable fuel. Reactor Core – structure containing all of the fuel elements. Moderator – material that slow down the neutrons (thermal neutrons) –Water – most common. Control Rods – control mechanism that absorbs neutrons to regulate the reaction. –Raised and lowered to control reaction –Contain neutron absorbing materials like boron or cadmium Nuclear Reactor Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed. Wilson,Buffa, College Physics, 4 th ed 2000 Prentice Hall

116. Pressurized Water Reactor Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed. Nuclear Power

117. Nuclear Fusion Combining two small nuclei into a larger nucleus For a given mass of fuel, a fusion reaction yields more energy than a fission reaction. Cutnell & Johnson, Wiley Publishing, Physics 5 th Ed.

118. Nuclear Fusion Challenge 2 smaller nuclei must be brought together so that the strong nuclear force will fuse them together. Both nuclei are positively charged so electrostatic repulsion must be overcome. Requires large kinetic energy  temperatures Fusion

119. Nuclear Fusion Uncontrolled fusion  Hydrogen Bomb –A fission reaction is used to initiate the fusion reaction. –Fission reaction is hot enough to fuse the hydrogen nuclei and cause fusion releasing even greater amounts of energy. Controlled fusion  Power Generation –Still under development (magnetic containment)

120. Nuclear Fusion Experimental Designs – Magnetic Containment Inertial Confinement Fusion Energy Wilson,Buffa, College Physics, 4 th ed 2000 Prentice Hall