Slide 1If you want to know your progress so far, please send me an email request at [email protected] ReviewReminder (for those who don’t read syllabus)26.9 Relativistic EnergyRelativistic Energy – ConsequencesEnergy and Relativistic MomentumProblem: relativistic protonSlide 9A photon is reflected from a mirror. True or false: (a) Because a photon has a zero mass, it does not exert a force on the mirror. (b) Although the photon has energy, it cannot transfer any energy to the surface because it has zero mass. (c) The photon carries momentum, and when it reflects off the mirror, it undergoes a change in momentum and exerts a force on the mirror. (d) Although the photon carries momentum, its change in momentum is zero when it reflects from the mirror, so it cannot exert a force on the mirror.Example 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 Resolution1101/14/1901/14/19General Physics (PHY 2140)Lecture 27Lecture 27 Modern PhysicsQuantum PhysicsBlackbody radiationPlank’s hypothesisChapter 27http://www.physics.wayne.edu/~apetrov/PHY2140/2201/14/1901/14/19If you want to know If you want to know your progressyour progress so far, please so far, please send me send me an email requestan email request at [email protected]@physics.wayne.edu3301/14/1901/14/19Lightning ReviewLightning ReviewLast lecture: 1.1.Modern physicsModern physicsRelativistic energy, momentumRelativistic energy, momentumRelativistic addition of velocitiesRelativistic 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?2 21mvpv c=-21ad dbabad dbv vvv vc+=+4401/14/1901/14/19Reminder (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…5501/14/1901/14/1926.9 Relativistic Energy26.9 Relativistic EnergyThe definition of The definition of kinetic energykinetic energy requires modification in requires modification in relativistic mechanicsrelativistic mechanicsKE = KE = mcmc22 – mc – mc22The term The term mcmc22 is called the is called the rest energyrest energy of the object and is of the object and is independent of its speedindependent of its speedThe term The term mcmc22 is 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 energy6601/14/1901/14/19Relativistic Energy – ConsequencesRelativistic Energy – ConsequencesA 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 mass E = mcE = mc22The 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 particles7701/14/1901/14/19Energy and Relativistic MomentumEnergy and Relativistic MomentumIt is useful to have an expression relating total energy, E, to the It is useful to have an expression relating total energy, E, to 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 = 0 and and E = mcE = mc22 Massless 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 10-31-31 kg = 0.511 MeV kg = 0.511 MeV8801/14/1901/14/19Problem: relativistic protonProblem: relativistic protonA proton in a high-energy accelerator is given a kinetic energy of A proton in a high-energy accelerator is given a kinetic energy of 50.0 GeV. Determine 50.0 GeV. Determine (a)(a)the momentum and the momentum and (b)(b)the speed of the proton.the speed of the proton.9901/14/1901/14/19A proton in a high-energy accelerator is given a kinetic energy of 50.0 GeV. A proton in a high-energy accelerator is given a kinetic energy of 50.0 GeV. Determine (a) the momentum and (b) the speed of the proton.Determine (a) the momentum and (b) the speed of the proton. Given:E = 50.0 GeV Find:p = ?v =?Recall that EE22 = p = p22cc22 + (mc+ (mc22))22. This can be used to solve for p:( ) ( )2 22 2 2 2E mc mc KE mcpc c- + -= =( )( )( )22250.9KE mc KEGeVpcc+= =Thus, Similarly with velocity:( )222 222111 1 0.9998EE mcmcv cEv cmcg g= � = =-� �= - =� �� �101001/14/1901/14/19QUICK 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 on (a) Because a photon has a zero mass, it does not exert a force on the mirror. the mirror. (b) Although the photon has energy, it cannot transfer any energy to (b) Although the photon has energy, it cannot transfer any energy 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 mirror, (c) The photon carries momentum, and when it reflects off the mirror, 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 momentum is 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