Modern Physics. The revolution!

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Morgan Nelson
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1 Modern Physics The revolution!

2 Creating a new theory is not like tearing down an old barn and erecting a skyscraper in its place. It is rather like climbing a mountain, gaining new and wider views, discovering unexpected connections between our starting point and its rich environment. But the point from which we started out still exists and can be seen, although it appears smaller and forms a tiny part of our broad view gained by the mastery of the obstacles on our adventurous way up.

3 Uncuttable?

4 The Atom Thompson proved in 1897 that cathode rays were particles from inside the a-tomos or un-cuttable atom Nagaoka pictured a planetary model for the atom, with electrons around a central mass

5 Plum Pudding Thompson instead supported Lord Kelvin s suggestion that electrons were embedded in a positively charged pudding Rutherford showed Nagaoka was correct by probing the atom with alpha particles

6 The Nuclear atom Rutherford s (Geiger- Marsden) results showed the atom is mostly empty space, with a very dense nucleus To see why, try firing cardboard pennies at copper pennies spaced out on your table

7 Data table for 50 shots # times Straight Through Slight Deflection Bounce Back IIII II

8 Ex 1: Use this to find the closest approach for 8.2 MeV alpha particles to a gold nucleus (to estimate outer limit of radius of nuclei) r m

9 The Bohr Atom Nils Bohr demonstrated the electrons in an atom are confined to particular energy levels. He called these levels orbitals Absorbing or emitting energy (a photon) causes the electron to jump between levels

10 Bohr s postulates Radiation is only emitted when the atom (electron) makes a transition from a higher to a lower energy state The difference in energy between the two states, ΔE = hf The angular momentum of the electron is quantized in units of h/2π (mvr=h/2π)

11 Electron in a box E k n 2 h 2 8m L e 2 For energy level n in a hydrogen atom, where L is the length of the box, aka orbital circumference, m e is the mass of the electron

12 Ex: use e in a box to find E 1 E k n 2 h 2 8m L e 2 For energy level n in a hydrogen atom, where L is the length of the box, aka orbital circumference, m e is the mass of the electron

13 This provided an explanation for the spectrum of electromagnetic radiation emitted from an excited atom It did not explain the relative intensity of spectral lines

14 Ex: find the wavelength of a photon absorbed for an n=1 to n=2 jump E E E 2 1 E 3.4eV ( 13.6eV ) E 10. 2eV

15 Ex: find the wavelength of a photon absorbed for an n=1 to n=2 jump E 10.2eV C hf c hc f E J s m s 1 c J m

16 Spectrum activity Sketch the spectrum for: Fluorescent light Hydrogen Neon Water

17 Photoelectric effect Photons above threshold frequency cause electrons to be emitted from metal plate Stopping potential allows us to measure kinetic energy of electrons

18 Einstein Einstein described light as a stream of particles called photons, each with an energy defined by their frequency E hf Ex 1: Find the energy of a radio photon from NL 610 AM (610 khz) E hf Js Hz E J

19 Ex 2: Find the energy of an Ultraviolet ray with frequency 5 x Hz E hf Js Hz E J

20 Work Function hf E max Maximum kinetic energy of photoelectron depends on the work function of the metal ϕ

21 Stopping Potential hf hf 0 ev Ex: The quantum nature of radiation

22 de Broglie de Broglie explained Bohr s model by describing the electron as a standing wave Only waves that have an even number of wavelengths are allowed Schroedinger took this further to describe the electron s location as a wave equation

23 de Broglie Ex: find the wavelength of an electron moving at 0.5c p h h p kg 34 Js m s m

24 Davisson-Germer Experiment

25 Davisson-Germer PhET

26 Davisson-Germer Experiment to find which of the following affect diffraction angles: Velocity Atom Separation Atom Radius Davison Germer Example

27 de Broglie Ex: find your wavelength! p h h p Js 105kg10m s m

28 What part of Don t you understand?

29 Schrodinger s model Electrons are like a wave with only certain wavelengths allowed The position is undefined, but a wave function ψ determines the probability of locating it

30 Schrodinger s cat

32 Ok, but what does an atom really look like?

33 Quantum Mechanics Quantum theory restricts predictions about the atomic world to probabilities Einstein and Bohr had many debates about this limitation Stop telling God God does not play dice what to do with the universe

34 No, not that Heisenberg That Heisenberg

35 Uncertainty principle xp h 4 Where Δx is the uncertainty in the position and Δp is the uncertainty in the momentum

36 Ex 1a: find the uncertainty in momentum An electron passes through a thin slit of width Δx = 23μm xp h 4 p h 4 x p J s m p kg m s 1

37 Ex 1b: what direction is the uncertainty in momentum, relative to the original direction of the electron beam? Perpendicular to beam direction

38 Uncertainty principle Et h 4 Where ΔE is the uncertainty in the change in energy and Δt is the uncertainty in the time that energy change occured

39 Ex 2: hydrogen atom

41 Isotopes Elements have a characteristic number of protons, e.g. Hydrogen always has one proton They may have different numbers of neutrons Neutrons help to glue together the nucleus of mutually repulsive protons

42 Radioactivity Marie and Pierre Curie discovered that some isotopes are unstable: they spontaneously decay and give off radiation

43 What are the effects of radiation?

44 Up and Atom!

45 You wouldn t like me when I m angry...

46 Radiation Radiation from the nucleus comes in three flavors: (Alpha): massive, slow, low penetration. He 2+ (Beta): fast, low mass, medium penetration. e - (Gamma): high energy E-M radiation AKA light. Gamma ray photon.

47 Nuclear equations Balance charge, then mass Ex: write the equation for the alpha decay of C

49 Activate the Radioactivity Activity Design a procedure to test the penetrating power of alpha, beta, and gamma radiation Record your results No, not an official IA. Just for phun

50 Radioactivity When a radioactive isotope decays, the amount remaining can be described by an exponential relation: N N e 0 t Where λ is the decay constant in disintegrations per second Ex: use this to derive a formula for half life

51 Ex: use this to derive a formula for half life N N 0 e t 1 T e ln 2 1 ln 2 T T ln 1 2 ln e T 1 2 T 1 2 ln 2

53 Half Life T 1/2 When a radioactive isotope decays, the amount remaining can be described by a half life relation: T 1 2 ln 2 Ex 1: find the decay constant for Ne-18, if it has a half life of 13s

54 Activity Level Ex: find the activity level if 350 atoms of C-14 decay to N- A 14 in 70 sec t N

55 Instantaneous Activity Level Ex: find the activity level if 2350 atoms of Ne-18 are remaining A N N e 0 t

56 Ex 1: find the amount remaining of 55kg of plutonium in the year 3009, if it has a half life of 8x10 7 a N N e 0 t kg

57 f(x)=100(0.5)^x % Remaining vs. Half-lives elapsed

58 Ex 2: Exponential decay Cesium 137 has a half life of 30 years. If 2.5 kg is left for 20 years, what mass will be left?

59 Ex 2: Exponential decay Cesium 137 has a half life of 30 years. If 2.5 kg is left for 20 years, what mass will be left? N N e 0 t A 1. 57kg

60 Ex 3: Exponential decay Cesium 137 has a half life of 30 years. If we start with 2.5 kg how much time passes until 0.32 kg remain? t 30a 0.32kg log 2.5kg 1 log 2 t 89a

61 Nuclear reactions Atoms can be broken up (fission) or combined (fusion) 2 1 H 3 1 H 4 2 He 1 n energy

62 Fission and Fusion We can release nuclear energy by fusing together lighter nuclei Or by breaking apart heavier elements

63 Ex: find the energy released by the fission reaction of U-235

64 Ex: find the energy released by the fission reaction of U n U Kr Ba 3( 1 n)

65 MeV MeV MeV (0) nucleon nucleon nucleon

66 Ex: find the energy released by the fission reaction of U MeV

68 Where does the energy come from? Einstein showed that in a nuclear reaction, some of the mass is converted into pure energy according to: 2 E mc Ex 1: how much energy is generated from 0.5g of Uranium? Ex2: how much energy is generated when 1kg of matter meets 1kg of antimatter?

69 Ex 1: how much energy is generated from 0.5g of Uranium? Ex2: how much energy is generated when 1kg of matter meets 1kg of antimatter? E 2 E mc kg E m 2 13 E mc 2 E 2.0kg E J m s J s

70 Harnessing Nuclear Power WWII arms race Oppenheimer: Manhattan Project Gadjet: test bomb July 16 th Little Boy: Enriched U-235 bomb: detonated over Hiroshima Aug. 6, Eq: 18 kt TNT (4.2x10 9 J per ton) cf May 1945 Germany Fat Man: Plutonium: detonated over Nagasaki Aug. 9, 1945

71 Modern thermonuclear weapons Thermonuclear weapons use a fission reaction to trigger a fusion bomb at the core This briefly reproduces the temperature and pressure conditions at the sun s core The highest yield is for hydrogen isotopes fusing to make helium, hence H bomb Soviets 1953 test bomb US 1954: 15 MT

Nuclear Fission Reactors To get safe, useful energy, we need: A chain reaction nb critical mass (50 kg Uranium, 16 kg Plutonium) A moderator to slow the neutrons down Control rods to

73 Nuclear Fission Reactors To get safe, useful energy, we need: A chain reaction nb critical mass (50 kg Uranium, 16 kg Plutonium) A moderator to slow the neutrons down Control rods to control the rate of the chain reaction, or stop it if necessary The CANDU reactor uses: Natural uranium instead of enriched (more U-235) Heavy water D 2 O as a moderator Cadmium control rods

76 Fusion Reactor? Nuclear fusion is more powerful, and cleaner: no radioactive fuel or waste! Fusion reactions are difficult to contain The Tokamak reactor uses magnetic fields to contain a plasma and generate fusion reactions Still not a stable energy producer

77 ITER: International Thermonuclear Experimental Reactor

78 Another option? We can use a "LASER" to heat up the hydrogen and ignite the fusion reaction

80 Proton-proton chain 2x0.42MeV 2x1.02MeV 2x5.49MeV 12.86MeV Total 26.72MeV

81 To be nuclear or not nuclear Create a presentation supporting your viewpoint Include pros and cons in terms of the ethical, financial, and environmental issues associated with nuclear energy

82 Mass Spectrometer Use the electric and magnetic forces to select a mass

83 First: Velocity Selector F F e B qe qvb v E B Only particles with the correct velocity continue to the next stage

84 Next: mass spectrometry F ma qvb mv r 2 m qbr v We can use this to separate isotopes

85 Nuclear quantization The excited Al-27 can release this energy as gamma photons either 1&2 or 3. Ex: find λ for 1

86 MeV MeV E J E hf J E E ch f c m

History and Structure of the Atom. From Democritus to...

1 History and Structure of the Atom From Democritus to... History of Atomic Theory 2 Democritus (from about 440 BC) coined the term atom which means uncuttable He felt that if you kept cutting matter smaller