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CU-Boulder ASTR 1020 - Quantum Mechanics

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ASTR 1020 1st Edition Lecture 4Quantum MechanicsEnergy levels of an atom- Ends of string can’t move- Only take half-integral waves- Only certain energies of electron are allowed. No other waves will fit- Add a dimension: 2—d waves on a surface like a drum- Add another dimension: 3-D wave patterns are complicated- Each has a different energyOur Star: The SUN99.9% of the mass of the Solar System***Q: What do we mean when we say that the sun is in gravitational equilibrium?A: There's a balance between the outward push of pressure+the inward pull of gravity1) How far away/big is the Sun?- Find the distance to an inner planet in AU- Direct distance measurement of that object- Once distance is known, size can be found2) What is the relationship between the Sun and the Earth?- How can we determine that the Earth revolves around the Sun?Why not a heliocentric model?Parallax –small shift in angular position when viewed from different places- The farther away something is, the smaller it’s parallaxNo stellar parallax is seen, so one of two possibilities must be true1. Earth is stationary, does not orbit Sun Geocentric model2. Stars are so far away that stellar parallax is too small to seestars must bevery far awayIn modern times, we can measure the Doppler shift of stars during different parts of our orbit= direct proof that we are the ones moving3)What is the Sun made of?- 91% Hydrogen, 8.9% Helium, 0.1% everything else4) How does the Sun produce its energy?5) How old is the Sun?- The great 19th century debate:o Evolutionists vs. Physicistso Charles Darwin vs. Lord KelvinQ: The Sun suddenly stops fusing hydrogen and loses its energy source. Which of the following is true?A: The core will start to collapseCould Sun be chemically burning?1. Energy released by burning oil ~10^7 joules/kg2. Solar energy output (Luminosity)= 3x10^26 joules/sec3. Need (3x10^26 joules/sec) / (10^7 joules/kg) = 3 x 10^19 kg/sec4. How long will the Sun last?Msun / amount burning per second(2 x 10^30 kg) / (3 x 10^19 kg/sec) = 7 x 10^10 sec=2000 yearsMaybe it’s shrinking?- Energy released from gravitation contraction can be ~10,000 times more powerfulthan chemical burningHow old can the Sun be if its source of energy is gravitational contraction?Use age from the chemical burning argument:10,000 x 2000 yr = 20,000,000 yearsBut geological record (Darwin) showed age of Earth to be 150,000,000 yearsEinstein provided the answer:E=mc^2Energy=massQ: Fusion in the Sun starts with 4 hydrogen nuclei (1 proton each) and ends with 1 helium nucleus (2 proton + 2 neutrons) AND energy. Which has more mass?A: 4 protonsNuclear Energy- Binding energy of nuclei varies- Binding energy of before/after nuclei may be different –thus masses different via E=mc^2ATOMS =smallest building bloc of matter (“invisible”) - Atomic number Z= number of protons determines kind of element- # protons = # electrons- Periodic Table lists each element in increasing atomic number- Mass number A= number of nucleons (protons + neutrons)Standard Model of Particle Physics- 12 particles + 4 forces + a few oddities - Quarks are bound together by Strong force (3 quarks =proton, neutron)- Leptons exist on their own (electrons, neutrinos)- “Gauge bosons” carry forcesFour Forces -What property does the force effect?- “color” holds nucleons together- “charge”- “flavor” changes quark flavors radioactivity- “mass” (not yet part of standard model)Building Atoms out of Quarks- everything is held together by Strong Forceproton = u+u+d neutron =u+d+dhydrogen = protondeuteron=p + n (isotope of hydrogen)tritium =p + 2n (isotope of hydrogenhelium isotopes 2 protons +1,2 neutrons Building atoms out of other atomsFission –big nucleus splits into smaller pieces (Nuclear power plants)Fusion –small nuclei stick together to make a bigger one (Star)Higher temperatures = more speed + fusionp-p chain fusion: Step 1• IN: 2 protons • OUT: deuterium, neutrino, anti-electron • (Need to do this twice) / (note one of the protons changes into a neutron)p-p chain fusion: Step 2 • IN: 1 deuterium 1 proton • OUT: 3He photon (gamma ray) • (Need to do this twice)p-p chain fusion: Step 3 • IN: two 3He nuclei• OUT: 4He, 2 protons (recycled)p-p chain fusion: Summary: • IN: 4 protons (H nuclei) • OUT: 1 4He nucleus, 2 photons (gamma rays), 2 positrons (anti-electrons), 2 neutrinosThe Sun –the theory- Ball of hydrogen 90% and helium 10%- Gravity crushes core to high pressures, temperatures- Thermonuclear fusion (p-p chain, 4H^4He) in the core for ~10 billion years- Energy from core fusion escapes and heats the rest of the star Neutrinos observed on Earth=direct evidence for fusion going on in the core (gravity in, pressure out)Neutrinos: Products of Nuclear Fusion in the Sun’s Core• Extremely small masses – travel close to speed of light • (Almost) don’t interact with other matter – requires lead wall 1 light year thick to stop a neutrino! – passes right through Sun and Earth without interacting(each p-p chain reaction produces 2 neutrinos)SOLAR NEUTRINO PROBLEM - Huge underground vat (500 tons) of dry-cleaning fluido Neutrino occasionally hits chlorine molecule, produces radioactive argon- Only collects 1 neutrino about every 3 days –even with 100,00 gallons Super-Kamiokandeuses 50,000 tons of water to capture neutrinosResults suggested neutrinos change “flavors” during course of flight to us (8 min)=Neutrino OscillationsSudbury Neutrino Observatory• Uses “heavy water” (some H in H20 replaced by its stable isotope deuterium) • SNO captures all three types of neutrinos (electron, muon, tao) – Detects the RIGHT numbers!!• “Solar neutrino problem” leads to big physics


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