If you want to know your progress so far, please send me an email request [email protected] ReviewReminder (for those who don’t read syllabus)26.9 Relativistic EnergyRelativistic Energy – ConsequencesEnergy and Relativistic MomentumProblem: relativistic protonA photon is reflected from a mirror. True or false: (a) Because a photon has a zero mass, it does not exert a force on theExample 1: Pair ProductionExample 2: Pair AnnihilationQuantum PhysicsIntroduction: Need for Quantum PhysicsDevelopment of Quantum Physics26.1 Blackbody RadiationBlackbodyBlackbody Radiation GraphWien’s Displacement LawThe Ultraviolet CatastrophePlanck’s Resolution1111/7/0311/7/03General Physics (PHY 2140)Lecture 27Lecture 27¾ Modern Physics9Quantum Physics9Blackbody radiation9Plank’s hypothesisChapter 27http://www.physics.wayne.edu/~apetrov/PHY2140/2211/7/0311/7/03If you want to know If you want to know your progressyour progressso far, please so far, please send me send me an email requestan email requestatatapetrovapetrov@[email protected]/7/0311/7/03Lightning ReviewLightning ReviewLast lecture:1.1.Modern physicsModern physics99Relativistic energy, momentumRelativistic energy, momentum99Relativistic addition of velocities221mvpvc=−21ad dbabad dbvvvvvc+=+Relativistic addition of velocitiesReview Problem:You are packing for a trip to another star, to which you will be traveling at 0.99c. Should you buy smaller sizes of your clothing, because you will be skinnier on the trip? Can you sleep in a smaller cabin than usual, because you will be shorter when you lie down?4411/7/0311/7/03Reminder (for those who don’t read Reminder (for those who don’t read syllabussyllabus))Reading Quizzes (bonus 5%):It is important for you to come to class prepared, i.e. be familiar with the material to be presented. To test your preparedness, a simple five-minute quiz, testing your qualitative familiarity with the material to be discussed in class, will be given at the beginning of some of the classes. No make-up reading quizzes will be given.There could be one today…… but then again…5511/7/0311/7/0326.9 Relativistic Energy26.9 Relativistic EnergyThe definition of The definition of kinetic energykinetic energyrequires modification in requires modification in relativistic mechanicsrelativistic mechanicsKE = KE = γγmcmc22––mcmc22The term The term mcmc22is called the is called the rest energyrest energyof the object and is of the object and is independent of its speedindependent of its speedThe term The term γγmcmc22is the is the total energytotal energy, E, of the object and depends , E, of the object and depends on its speed and its rest energyon its speed and its rest energy6611/7/0311/7/03Relativistic Energy Relativistic Energy ––ConsequencesConsequencesA particle has energy by virtue of its mass aloneA particle has energy by virtue of its mass aloneA stationary particle with zero kinetic energy has an energy A stationary particle with zero kinetic energy has an energy proportional to its inertial massproportional to its inertial massE = E = mcmc22The mass of a particle may be completely convertible to The mass of a particle may be completely convertible to energy and pure energy may be converted to particlesenergy and pure energy may be converted to particles7711/7/0311/7/03Energy and Relativistic MomentumEnergy and Relativistic MomentumIt is useful to have an expression relating total energy, E, to It is useful to have an expression relating total energy, E, to the the relativistic momentum, prelativistic momentum, pEE22= p= p22cc22+ (mc+ (mc22))22When the particle is at rest, When the particle is at rest, p = 0p = 0and and E = mcE = mc22Massless particles (Massless particles (m = 0m = 0) have ) have E = pcE = pcThis is also used to express masses in energy unitsThis is also used to express masses in energy unitsmass of an electron = 9.11 x 10mass of an electron = 9.11 x 10--3131kg = 0.511 kg = 0.511 MeVMeV8811/7/0311/7/03Problem: relativistic protonProblem: relativistic protonA proton in a highA proton in a high--energy accelerator is given a kinetic energy of energy accelerator is given a kinetic energy of 50.0 50.0 GeVGeV. Determine . Determine (a)(a)the momentum and the momentum and (b)(b)the speed of the proton.the speed of the proton.9911/7/0311/7/03A proton in a highA proton in a high--energy accelerator is given a kinetic energy of 50.0 energy accelerator is given a kinetic energy of 50.0 GeVGeV. . Determine (a) the momentum and (b) the speed of the proton.Determine (a) the momentum and (b) the speed of the proton.Recall that EE22= p= p22cc22+ (mc+ (mc22))22. This can be used to solve for p:() ()2222 2 2Emc mcKEmcpcc−+−==Given:E = 50.0 GeVFind:p = ?v =?Thus, ()()()22250.9KE mc KEGeVpcc+==Similarly with velocity:()222222111 1 0.9998EEmcmcvcEvcmcγγ=⇒= =−=− =101011/7/0311/7/03QUICK QUIZA photon is reflected from a mirror. A photon is reflected from a mirror. True or falseTrue or false: : (a) Because a photon has a zero mass, it does not exert a force (a) Because a photon has a zero mass, it does not exert a force on on the mirror. the mirror. (b) Although the photon has energy, it cannot transfer any energ(b) Although the photon has energy, it cannot transfer any energy to y to the surface because it has zero mass. the surface because it has zero mass. (c) The photon carries momentum, and when it reflects off the mi(c) The photon carries momentum, and when it reflects off the mirror, rror, it undergoes a change in momentum and exerts a force on it undergoes a change in momentum and exerts a force on the mirror. the mirror. (d) Although the photon carries momentum, its change in momentum(d) Although the photon carries momentum, its change in momentumis zero when it reflects from the mirror, so it cannot exert a is zero when it reflects from the mirror, so it cannot exert a force on the mirror.force on the mirror.(a)(a)False False (b)(b)False False (c)(c)True True (d)(d)FalsepFt∆=False111111/7/0311/7/03Example 1: Pair ProductionExample 1: Pair ProductionAn An electronelectronand a and a positronpositronare produced and the photon are produced and the photon disappearsdisappearsA positron is the antiparticle A positron is the antiparticle of the electron, same mass of the electron, same mass but opposite chargebut opposite chargeEnergy, momentum, and Energy, momentum, and