1Lecture 10Reminders:Reading prior to this lecture TZD 2.4-2.9Reading for this week TZD Chapter 3 (many topics, some not covered in lecture)Homework #3 due this WednesdayExam #1 will be Friday, September 25 in class.Details to be discussed todayToday’s topics: Relativistic massExam #1 will be in class on Friday, September 25, 2009.• Please make sure to attend on time so everyone will have the full 50 minutes to take the exam.• The exam will cover all the material on special relativity as presented in the assigned textbook reading, lecture notes, and homework #1-#3.• The exam is closed book. A formula sheet will be included with the exam (which you can preview on the class web page). Calculators are allowed, but no use of stored equations.• The exam will consist of 4-6 problems – some explanation, some problem solving…• A practice exam will be available under the Exam link on the class web page.mupuγ=ABParticle A has half the mass but twice the speed of particle B. If the particles’ momenta are pAand pB, thenA. pA> pBB. pA= pBC. pA< pBγuis bigger for the faster particle. Thus in special relativity particle A has a larger momentum.Clicker questionClassically, both particles have the same momentum.But in special relativity:Chemical ReactionsA simple example is the combustion of hydrogen and oxygen, which is a commonly used reaction in rocket engines:2H2+ O2→ 2H2O + heatThe result is simply water vapor.M(H2O) = 18.0153 g/mol M(O2) = 31.9988 g/mol M(H2) = 2.0159 g/mol Mass difference 5 x 10-12kg (too small to calculate without more digits!) E=mc2Æ 4.8 x 105Joules / mol of reactionIf: 2H2(g)+ O2(g)Æ 2H2O(g) ΔH°rxn= -482 kJ/molIf: 2H2(g)+ O2(g)Æ 2H2O(g) ΔH°rxn= -482 kJ/molNuclear Reactions have a lot more mass energy exchanged than chemical reactions. Chemical as well as nuclear reactions in which energy enters or exits results in a corresponding change in mass. The energy stored in chemical or nuclear bonds shows up in mass. Breaking the bonds releases energy and lowers the total massSuppose the speed of light in the universe was reduced a factor of 2 but nothing else changes. What would be the change in the quantity of firewood to be burned to maintain the same level of output heat?A. Same quantity as beforeB. Half as much firewood needs to be burnedC. Twice as much firewood needs to be burnedD. One quarter as much firewood needs to be burnedE. Four times as much firewood needs to be burnedClicker question2Physicists often get weary from keeping track of so many large and small numbers.So, they invent other unit systems that are more convenient.One electron-Volt of energy is the amount of energy requires to move a single electron across one Volt of potential difference. 1 eV = 1.6 x 10-19JoulesThink about why that value looks familiar.A proton has a mass of 938 MeV/c2. What is this in kg?()kg 1067.1m/s 103.00J/eV 1060.1eV 10938/MeV 93827281962 −−×=××⋅×=cEnergy unit are eV.Momentum units are eV/cMass units are eV/c22222)()( mcpcE+=Recall our equation:42222cmcpE +=Conservation of energy requires that the sum of the photon energies equal the total π0energy.MeV 700MeV 500MeV 200)()()(210=+=+=γγπEEEAlthough we don’t need it, we can see that the π0kinetic energy is KE = E – mc2= 700 MeV – 135 MeV = 565 MeVCan get velocity from2)/(11cv−=γ2mcE=γ2mcEγ=Fromwe note thatA π0particle decays into two photons. The photon energies are measured to be 200 MeV and 500 MeV. The π0rest mass is 135 MeV/c2. What is the π0velocity?What is the velocity of a π0with rest mass 135 MeV/c2and total energy 700 MeV?2.5MeV 135MeV 700/MeV135MeV 700222==⋅==ccmcEγObtaining velocity from 2)/(11cv−=γ22)/(11 cv=−γ2)/(11cv−=γ1)/(12=− cvγ⇒211γ−=cv⇒⇒221)/(1γ=− cv⇒γ1)/(12=− cv⇒For this problem, 98.096.02.5111122==−=−=γcvSo the π0velocity was 0.98cEnd of special relativity… End of material covered on Exam #1.For those interested beyond the class, The Fabric of the Cosmos: Space, Time, and the Texture of Realityby Brian Greene is a fascinating read.3Why is the atom so important?Special relativity has effects that are typically not observable except when objects move very fast (close to the speed of light).One exception is rest mass energy which exists no matter what the speed.Quantum mechanics has effects that are typically not observable except when objects are very small (like atomic sizes).Thus, the development and understanding of quantum mechanics is intimately tied to the discovery and understanding of the atom.A useful picture of atomsThe center of the atom is composed of protons and neutrons bound together in a very small nucleusNuclei radii range from about 1 to 8 fermi (1 fermi = 1 fm = 1x10-15m)The rest of the atom is basically empty with electrons flying around.The electrons extend out to ~0.1 nm, aka 1 ångström (1 Å)Electrons have q=−1.6x10-19C and protons have q=+1.6x10-19C.Protons and neutrons have about the same mass (938.3 MeV/c2and 939.6 MeV/c2); electrons are ~1800 times lighter (0.511 MeV/c2).A useful picture of atomsAtomic number Z gives # of protons (and # of electrons for a neutral atom).Atomic mass number A gives number of nucleons (protons + neutrons)The actual atomic mass is not just the sum of the masses of protons, neutrons, and electrons. Why?Binding energy (of protons and neutrons together) reduces the mass.Atomic mass unit u is used to measure atomic masses. It has a value of 931.5 MeV/c2.When protons and neutrons fuse (nuclear fusion) energy is released (which is made up for by the loss of mass). This is what powers the sun (and the hydrogen