Physics 4 – April 27, 2017 P3 Challenge – Show how the quark composition for a neutron predicts no charge.

Objectives/Agenda/Assignment 12.1 Matter and Light Assignment: p502 #1-23 Agenda: Wave/particle duality Momentum of light Photoelectric effect Matter waves Electron diffraction

Wave particle duality Matter Particles Waves Light Atoms Stoichiometry Lots of experiments!!! Double slit experiment works for beams of electrons!!! Photoelectric effect – Light on metal ejects electrons depending on frequency, not intensity Electromagnetic Radiation Ray diagrams, Reflection, refraction, mirrors, lenses Double Slit Expt – Proves waves

Photoelectric Effect Wave Model predictions: The intensity of the radiation should have a proportional relationship with the resulting kinetic energy. The photoelectric effect should occur for any light, regardless of frequency or wavelength. There should be a delay on the order of seconds between the radiation’s contact with the metal and the initial release of photoelectrons. (time for energy to build up) http://phet.colorado.edu/en/simulation/photoelectric

Photoelectric Effect Experimental result: The intensity of the light source had no effect on the kinetic energy of the photoelectrons. Kinetic energy of the photoelectrons depends on the frequency of light used. Below a certain frequency, the photoelectric effect does not occur at all. There is no significant delay (less than 10-9 s) between the light source activation and the emission of the first photoelectrons.

Photoelectric effect hf =  + Ek The energy of the photon of light must be equal to the work function, , of the metal. Any excess energy results in the form of kinetic energy of the electron that is ejected from the metal. E is measured with the stopping voltage for a given metal and frequency. Ek is then eV, the charge on an e times the stopping voltage.

Momentum of light Even though photons has no mass, they nevertheless have momentum. Some observable evidence of this is the momentum that is delivered to a space sail from “solar wind”. Solar wind is light. But that light can collide with a sail and deliver some momentum, even though light is massless. Special relativity provides some insight: E2 = p2c2 + m2c4 For a massless particle, this is E = pc. p = E/c = hf/c (c=f so 1/ =f/c) p=h/  The momentum of light depends on the wavelength of light.

The Wave Nature of Matter Louis de Broglie posited that if light can have particle properties, matter should exhibit wave properties. http://www.youtube.com/watch?v=DfPepr Q7oGc Dr. Quantum De Broglie proposed that the relationship between mass and wavelength was p = h mv

Matter waves DeBroglie proposed that particles have a wave nature and a corresponding wavelength given by 𝝀= 𝒉 𝒑 = 𝒉 𝒎𝒗 Echoes the momentum of light: p=h/ Davisson-Germer found that beams of electrons diffract producing an interference pattern with 𝐧𝝀=𝒅𝒔𝒊𝒏𝜽 The wavelength observed in the diffraction experiment agrees with the wavelength predicted based on the mass of an electron. This confirms the theory of the wave nature of particulate matter.

Describing matter waves - QM The Bohr model of the atom with quantized levels can be explained by using quantized angular momentum. 𝒎𝒗𝒓= 𝒏𝒉 𝟐𝝅 h/2 is so common in QM that it is known as h (h-bar) This assumption leads to the observed energy levels for the hydrogen atom that were described by Rhydberg. 𝑬=− −𝟏𝟑.𝟔 𝒏 𝟐 eV Give the energy of an electron in energy level n in units of eV.

The wavefunction - orbitals The matter wave of the electron within the hydrogen atom has been completely described. This two body system can be solved. No other system (3+ particles) is able to be solved with our current level of computational ability. We assume that all other atoms have similar solutions The wavefunction exists in space-time and describes the probability of finding an electron in a given volume of space. 𝑷 𝒙,𝒕 = 𝚿(𝒙,𝒕) 𝟐 𝚫𝑽

Uncertainty principle With Newtonian mechanics, if we know the initial conditions of a physical system, we can calculate the conditions of the system at some later time. Recall all of the kinematics, dynamics and energy calculations we have done to do this. We cannot do the same with small particles, because of their wave duality. We can’t exactly know the position and momentum of a particle. There will always be a finite uncertainty, a theoretical limit to how good your measurements can be: 𝚫𝒙𝚫𝒑≥𝒉/𝟒𝝅 Also 𝚫𝑬𝚫𝒕≥𝒉/𝟒𝝅

Tunneling Consider an electron that is confined to a “box”: a region of space in the x dimension. The wavefunction for the electron will have a probability that is large within the box. But unlike a particle that’s confined to a box, a wavelike particle has a small probability that it will be located on the other side of the barrier. An important application of this phenomenon is the Scanning Tunneling Electron Microscope which is able to use an electron beam that tunnels into the surface of other atoms. In this way we can take pictures of atomic scale items.

Exit slip and homework Exit Slip – What is the wavelength associated with a proton moving at 7.3 x 106 m/s? What’s due? (homework for a homework check next class) p502 #1-23 What’s next? (What to read to prepare for the next class) Read 12.1, 12.2