Electromagnetic radiation behaves as particles 1. Notes of the problem discussed Tuesday. 2. Quiz 9.11 and a few comments on quiz Topics in EM waves as particles:  Blackbody radiation and Planck’s constant, Planck’s Nobel Prize in physics.  The Photoelectric Effect and Einstein's Nobel Prize in physics.  The X-rays and Roentgen’s Nobel Prize in physics.  The Compton Effect and Compton’s Nobel Prize in physics.  Pair production, energy to mass conversion and Anderson’s Nobel Prize in physics.  The wave-particle duality and the door to yet another new world. today Tuesday

One page review of Special Relativity S and S’ system: S and S’ system: For a particle with velocity in S: For a particle with velocity in S: The Doppler effect: The Doppler effect: S’ moves with velocity v in S along the x-axis. When =0, the course is moving away from the observer. When θ =0, the course is moving away from the observer.

problem 33, page 64 Step 1, choose reference systems Step 1, choose reference systems Step 2, interpreter proper length and time in their systems Step 2, interpreter proper length and time in their systems in S:in S’: Ground: S On the muon: S’ Solve it in S: The time it takes the muons to cover the distance L 0 : Now verify: is verified. So Solve it in S’: The time it takes the muons to cover the distance L : Since and is verified.

The Compton Effect When two waves meet, they superposition each other. When two particles meet, they collide. When two waves meet, they superposition each other. When two particles meet, they collide. When X-rays meet electrons  Compton scatter, behave exactly as two particles collide: When X-rays meet electrons  Compton scatter, behave exactly as two particles collide: The energy of a photon with frequency f is: So its momentum The energy of a photon with frequency f is: So its momentum In the x-ray electron system, the initial momentum is In the x-ray electron system, the initial momentum is The final moment is The final moment is x -component y-component Based on moment conservation: Based on moment conservation: And energy conservation: And energy conservation: Solve the above three equations (all algebraic manipulation) We have: Solve the above three equations (all algebraic manipulation) We have: y x hint

Example 3.3 Compton scattering and incident photon’s wavelength is known. Asked: momenta of incident photon, scattered photon and the electron. Relevant formulas and concept: Work on the blackboard. Momentum conservation

Example 3.4 Employ energy and momentum conservation laws. Work on the blackboard.

Pair production, energy to mass conversion When photon with energy above the rest mass of two electrons ( ) interact with the electric field of a nucleus, this photon may be turned into a pair of electron and positron. This process is called pair production through which energy gets turned into mass. When photon with energy above the rest mass of two electrons ( ) interact with the electric field of a nucleus, this photon may be turned into a pair of electron and positron. This process is called pair production through which energy gets turned into mass. Positron is the anti-particle of electron: it has the same mass as an electron but the opposite charge. Positron is the anti-particle of electron: it has the same mass as an electron but the opposite charge. When a particle and anti-particle meet, they annihilate into a photon, the process that mass converts into energy. When a particle and anti-particle meet, they annihilate into a photon, the process that mass converts into energy. Example 3.5: energy conservation. Example 3.5: energy conservation. What is the B-field direction?

Pair production in a bubble chamber What is the magnetic field direction? What is the magnetic field direction? electron positron

The wave-particle duality Wave or particle? Depends on the wavelength ( ) and the dimensions ( ) in your experiment. Wave or particle? Depends on the wavelength ( ) and the dimensions ( ) in your experiment. The double-slit experiment The double-slit experiment Wave Particle as Wave

Example 3.6 How do we solve this problem? How do we solve this problem? For (c), from We calculate the power intensity at this place, and then repeat the procedures in (a). For (a), we have wavelength and the power intensity, and this formula: The number of photons is what in the question. For (b), the minimum at the interference pattern has no light  no photons

Review questions List the arguments in this chapter that photon is a particle. List the arguments in this chapter that photon is a particle. List the arguments in this chapter that photon is a wave. List the arguments in this chapter that photon is a wave. When you treat photon as a wave? When as a particle? When you treat photon as a wave? When as a particle?

Preview for the next class Text to be read: Text to be read: In chapter 4: In chapter 4: Section 4.1 Section 4.1 Section 4.2 Section 4.2 Section 4.3 Section 4.3 Questions: Questions: What is the Bragg Law? What is the Bragg Law? An electron is a particle. One cannot have half an electron. How do you interpret the amplitude of an electron wave? An electron is a particle. One cannot have half an electron. How do you interpret the amplitude of an electron wave? What is the form of the Shroedinger equation for free particle? What is the form of the Shroedinger equation for free particle?

Homework 5, due by 9/23 1. Problem 31 on page Problem 35 on page Problem 40 on page Problem 42 on page 94.