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Physics 102, Class 25 The Atomic Nucleus and Radioactivity 11/30/2005 Quantum Mechanics Review • The PHOTOELECTRIC EFFECT can only be understood if light has a particle nature • At small scales, everything has both a particle nature and a wave nature • The particle nature is usually seen in INTERACTIONS, the wave nature is usually seen in PROPAGATION Quantum Mechanics Review • TWO BIG RULES for the Wave Nature: – Energy is proportional to frequency, E=hf – Momentum is inversely proportional to wavelength, (mv)=h/wavelength • On the exam I will give you – – – – v=wavelength x frequency E=hf (mv)=h/wavelength and the value of h, (if needed) Quantum Mechanics Review • Matter Waves give you PROBABILITIES, not CERTAINTIES • The two UNCERTAINTY PRINCIPLES comes from thinking about standing waves in a box – Δ(mv) x Δx is greater than or equal to hbar – ΔE x Δt is greater than or equal to hbar • The QUANTIZED ENERGY LEVELS seen in atoms come from thinking about standing waves around a nucleus. These explain the discrete light spectra from atoms. CPS Question • Energy levels in atoms are discrete because – A: electrons can orbit at any distance from the nucleus – B: only certain numbers of electrons are permitted – C: the electron’s wave function needs to be a standing wave CPS Question • Energy levels in atoms are discrete because – A: electrons can orbit at any distance from the nucleus – B: only certain numbers of electrons are permitted – C: the electron’s wave function needs to be a standing wave The Beginning of ““Radioactivity”: Radioactivity”: X -Rays X-Rays • Let’s apply what we learned in Quantum Mechanics to Heavier Atoms • We can get insight into: – The sizes of Atoms – The origin of X-rays CPS Question • X-Rays are associated with – A: Transitions of outer electrons – B: Transitions of inner electrons CPS Question • X-Rays are associated with – A: Transitions of outer electrons – B: Transitions of inner electrons The Beginning of ““Radioactivity”: Radioactivity”: Uranium • Uranium: Who was Uranus? – It’s the name given to the 7th planet outwards from the Sun learn more: http://solarsystem.nasa.gov/planets Wait a Minute, Look Closer at this Picture • All the “dot” sizes are about the same! learn more: http://solarsystem.nasa.gov/planets Wait a Minute, Look Closer at this Picture • All the “dot” sizes are about the same • We learned about diffraction of light passing through a narrow slit • This dot size is created by diffraction of the light entering the telescope learn more: http://solarsystem.nasa.gov/planets Uranium • Uranium: Who was Uranus? – In Greek Mythology, the Titans, who came before the Olympian gods, were the children of Uranus (male) and Gaea (female) Cronus, a hungry Titan painting by Goya learn more at: www.timelessmyths.com/classical/titans.html Uranium image from: http://www.molres.org/MRI_Downloads.html All Atoms Heavier than Lead are Radioactive image from: http://www.molres.org/MRI_Downloads.html Originally, There Were Three Known Types of Radiation • Alpha – These were used by Rutherford’s group to find out that atoms had nuclei. Alpha particles are helium nuclei, so they are heavy and have a positive charge. • Beta – These were the “cathode rays” studied by JJ Thomson. They are electrons, so they are light and have a negative charge. • Gamma – This is electromagnetic radiation, like visible light, but at frequencies even higher than X-rays. They are emitted from nuclear transitions. Gamma rays are massless and have no charge. Radioactivity Comes from the Nucleus of the Atom • Nucleus: – made of protons and neutrons – Held together by the “strong nuclear force” – makes up almost all the weight of the atom – tiny, 10-14 to 10-15 meter radius – like a liquid drop (surface tension) image from http://http://jazz.physik.unibas.ch/~krusche/nucleus.gif Gamma Rays Come from Transitions Between Nuclear Energy Levels • quantum mechanics gives the nucleus an internal shell structure, analogous to electrons in atom • when electrons in the atom change from one quantized energy level to another, they emit or absorb photons (X-ray or lower frequency) • when the nucleus changes from one quantized energy level to another, it emits or absorbs photons (Gamma Rays) CPS Question • Radioactivity originates from – the electrons in the atom – the nucleus of the atom CPS Question • Radioactivity originates from – the electrons in the atom – the nucleus of the atom Alpha and Beta Particles • Alpha particles pick up speed as they go away from the nucleus • Beta particles slow down as they go away from the nucleus Quarks • There are something like 200 different particles known now • This big zoo of particles comes from different combinations of six “Quarks” • The six types: – Up, Down, Strange, Charm, Top, Bottom Go UNM! • The name “Quark” comes from Finnegan’s Wake • the person who coined the name, Murray Gell-Mann (Nobel prize winner), founded the Santa Fe Institute and teaches at the UNM physics department! image from: http://www.bhm.ch/auxx/galerie_nachtderphysik/gross/Murray_Gell-Mann.jpg Albuquerque Isotopes • Isotopes have special meaning in Albuquerque Non -Albuquerque Isotopes Non-Albuquerque • An element always has a certain number of PROTONS – the number of electrons equals the number of protons – all chemistry and material properties are defined by the number of electrons • But an element can have different numbers of NEUTRONS – all have the same chemistry and material properties • All the different versions of an element are called “Isotopes” of the element Example: Isotopes of Hydrogen • 1 proton+0 neutrons – normal hydrogen, most abundant, not radioactive • 1 proton+1 neutron – called “deuterium”, ingredient in “heavy water”, not radioactive • 1 proton+2 neutrons – called “tritium” – is radioactive image from: http://images.encarta.msn.com/xrefmedia/aencmed/targets/illus/ilt/T046738A.gif Example: Isotopes of Hydrogen • All of these isotopes have almost exactly the same chemical and material properties, because those properties only depend on the electrons image from: http://images.encarta.msn.com/xrefmedia/aencmed/targets/illus/ilt/T046738A.gif Why Nuclei Fall Apart • Protons REPEL each other by the electrical force – works at all distances • Protons and Neutrons ATTRACT other Protons and Neutrons by the “strong nuclear force” – only works at short distances • If the nucleus gets big enough, then the protons that are farther apart are REPELLED more by the electrical force than they are ATTRACTED by the nuclear force – if it has the opportunity, the nucleus would like to split into smaller pieces Nuclei are Not Usually Round • The nuclei have to find the best way to balance out the electrical and nuclear forces, so they are usually either “Prolate” or “Oblate” images from http://en.wikipedia.org/wiki/Spheroid CPS Question • Nuclei can fall apart because – A: The strong nuclear force can become bigger than the electrical force for large nuclei – B: The strong nuclear force can become smaller than the electrical force for large nuclei CPS Question • Nuclei can fall apart because – A: The strong nuclear force can become bigger than the electrical force for large nuclei – B: The strong nuclear force can become smaller than the electrical force for large nuclei What is ““Half-Life”? Half-Life”? • An unstable nucleus has a constant probability per time of decaying – probability of decay=constant x time • The “half-life” is how much time is required for 50% probability of decay CPS Question • Let’s say we start with a sample of an unstable isotope. After 1 “half-life”, 50% of the unstable nuclei have decayed, so 50% of the sample remains. How much of the original sample remains after 2 “half-lives”? – – – – – A: zero B: 25% C: 50% D: 75% E: Can’t say CPS Question • Let’s say we start with a sample of an unstable isotope. After 1 “half-life”, 50% of the unstable nuclei have decayed, so 50% of the sample remains. How much of the original sample remains after 2 “half-lives”? – – – – – A: zero B: 25% C: 50% D: 75% E: Can’t say CPS Question • If we have two radioactive samples that both decay by emission of alpha particles, which one will be “hotter”? – A: the one with the longer half-life – B: the one with the shorter half-life CPS Question • If we have two radioactive samples that both decay by emission of alpha particles, which one will be “hotter”? – A: the one with the longer half-life – B: the one with the shorter half-life What ’s Left After the Nucleus Decays? What’s • You can figure it out by how much charge is emitted in the decay: – If + charges are emitted, the atomic number goes down by the number of + charges – If – charges are emitted, the atomic number goes up by the number of – charges – If neutrons are emitted, the atomic mass goes down by the number of neutrons – If gamma rays are emitted, atomic number and atomic mass stay the same • “Transmutation” is the name for changing one element into another. Carbon -14 Dating Carbon-14 • High energy radiation from space interacts with the upper atmosphere, transmuting nitrogen to carbon-14, which is radioactive • Carbon is an essential part of life on Earth, and a small but constant part of the carbon in every living thing is this radioactive carbon-14 • After the plant or animal dies, it stops taking in the carbon-14. We can determine the year of death from the half-life of the carbon-14, or from the ratio of carbon-14 to carbon-12. Radiation and Health • High-energy radiation can knock electrons off of atoms and molecules in the body. • This causes new molecules to form. Some of them are useless and some of them are harmful. • Because of the continuous background radiation that we are all exposed to all the time, life has repair mechanisms that can cope with radiation received at constant low levels. • Radiation at high levels will overwhelm the body’s natural defenses. • Natural background radiation exposure is about equal to medical and dental X-rays, and these two together are about 97% of all the radiation people are usually exposed to. Assignments • Reading and Homework assignments are listed on “Course Schedule” web page.