1Chapter 31Light Quanta22Particles and Waves• Particles have mass and obey Newton’s Laws–They travel through space• Waves interfere, refract and diffract–The extend across space• Particles and waves seem to be mutually exclusive• However, light has properties that made it difficult to classify– The question was pondered for 2000 years33The Quantum• Max Planck hypothesized that energy from warm bodies was emitted in discrete energy bundles• The fundamental unit of this energy is called a quantum• The energy of each quanta of energy is determined by the frequency of the radiation44What?!?!• Stop and think about the last slide: energy only comes in discrete units• That means that it is either all or nothing…– You can never have half of this fundamental unit of energy• This is like saying that when you run, you can either run at a speed that lets have n units of energy or n+1 units– You can’t have a velocity in between!55Planck’s Constant• The relationship between a quanta of energy and the frequency of the emitted radiation is:• This packet of energy of light is called a photon• When we want to talk about the energy of nphotons:JshhfE34106.6−×==nhfE =Note that mass never comes into the energy equation.66Problem Solving: Planck’s Constant• What is the energy of one photon with a frequency of 4*1014Hz (red light)?• What is the energy of 10 photon’s with a frequency of 7.5*1014Hz (blue light)?JHzJshfE1914341064.2)104)(106.6(−−×=××==JHzJsnhfE1814341095.4)105.7)(106.6)(10(−−×=××==77The Photoelectric Effect• When light hits metal, we would expect the photons to be able to give energy to the electrons, eventually enough to eject them88Classical Expectations for the Photoelectric Effect• Classical physics expects that there will be a delay between when the light shines on the metal and the ejection of the electrons (to allow the build up of energy)– There will be a longer delay for the lower frequencies of light because these have lower energies.• We would also expect that we will get more energetic electrons when be shine more light (photons) on the metal99Actual Observations From the Photoelectric Effect•There was no connection between the time lag for the ejection of electrons and the brightness or frequency of light• The effect was observed with violet and ultraviolet light but not red light• The rate electrons were ejected was proportional to the brightness of the light• The maximum energy of the light was not affectedby the brightness of the light but it did depend on the frequency of the lightThese result supported Planck’s quantum theory.1010Wave-Particle Duality• The photoelectric effect showed that light also has particle properties– All of the energy of a photon is absorbed, if light was only a wave, only that energy in the part of the wave the interacts with the electron would be imparted to the electron• Therefore, light has properties of bothparticles and waves!1111The Double Slit Experiment• Let us reconsider Young’s double slit experiment from the photon point of view• Use a dim light source so that we effectively have only one photon at a time hits the double slit and let the light be projected onto photographic film• We will see the same diffraction pattern over time, the pattern is built up one photon at a time1212The Double Slit Experiment with Photons1313Electron Diffraction• If light can have both particle and wave properties, can object we regard as particles also have wave properties?• Let’s redo the double slit experiment with a beam of electrons…• We see a similar double slit diffraction pattern• If the electron had only particle properties, we would see only two spots behind the slits1414The de Broglie Wavelength• So, what is the wavelength of an electron?• It is important to note why we do not usually encounter the wave nature of the matter around us– Quantum effects are only noticeable on extremely small scale. If our everyday life,we do not notice quantum effects because the length scales we live in are so large.– You can think of it as noticing a change in mass of the Earth if a gain of sand suddenly disappeared! Or noticing that g changed because of this missing grain of sandmomentumh wavelength =1515Problem Solving: de Broglie Wavelength• What is the wavelength of an electron that has a velocity 5 m/s?msmkgJsmomentumhWavelengthsmkgsmkg4303431-311045.1/*1055.4106.6/*1055.4)/5)(10(9.11 mv momentum−−−−×=××==×=×==1616Uncertainty Principle• If an electron is a wave, how well can be measure it position (if it is a wave it will be dispersed in space)• If we probe an electron, we know we must impart at least one quantum of energy to the system, therefore the system is affect by the measurement• Because of this, there is always an uncertainty in measurement in the quantum domain:π2 htExp=≥∆∆≥∆∆1717Problem Solving: Uncertainty Principle• If we know the location of an electron to within 1nm, how well can we know it momentum?smkgmJsxhpxp/*101)101(2106.6225934−−−×=××=∆=∆∆≥∆ππ1818Problem Solving: Uncertainty Principle• If we know the energy of an electron to within 1 J, how well do we know its lifetime?sJJsEhtEt34341011**2106.62−−×=×=∆≥∆∆≥∆ππ1919Correspondence• We have stated before that quantum physics applies only to small scales• Correspondence states that any theory on very small scales (or very large scales) must agree with classical physics in our everyday domain• This means that the laws of physics that are true in the quantum domain must also be true in our