Wave-Particle Duality of Light, Lecture notes of Chemistry

Download Wave-Particle Duality of Light and more Lecture notes Chemistry in PDF only on Docsity! ________________________________________________________________________________ ________________________________________________________________________________ 5.111 Lecture Summary #3 Monday, September 8, 2014 Reading for today: Section 1.2 and Section 1.4 with a focus on pgs 10-12 (4th ed or 5th ed). Read for Lecture 4: Section 1.5 – The Wave-Particle Duality of Matter, and Section 1.6 – The Uncertainty Principle. (Same sections in 4th ed. or 5th ed.) Topics: The wave-particle duality of light I. Light as a wave, characteristics of waves II. Light as a particle, the photoelectric effect With the discovery of subatomic particles, the need for a new type of mechanics (Quantum mechanics) began to emerge. To explain the observations that scientists were making, two tenets were required: 1. Radiation and matter display both wavelike and particle-like properties; and 2. Energy is quantized into discrete packets (called photons). THE WAVE-PARTICLE DUALITY OF LIGHT LIGHT AS A WAVE; CHARACTERISTICS OF WAVES Waves have a periodic variation of some quantity. Water Wave Sound Wave + _ Average level High level Low level + _ Average density High density Low density Light We can characterize electromagnetic radiation (or any wave) in terms of: Amplitude (a): the deviation from an average level. Can have (+) or (-) value. Wavelength (λ axima or minima Frequency (ν): the num + _ positive amplitude negative amplitude λ 1 radiation) is the periodic variation of an electric field.( between successive m ): the per unit timeber of 1/ν e for one cycle to occur Units of frequency (ν I We can calculate the speed of a wave: Speed = distance traveled / time elapsed = = Electromagnetic radiation has a constant speed, c (the “speed of light”). c = λ ν = -1 For any wavelength of light, the product of λ * ν is always c. λ and ν are NOT independent of each other. If you know λ, you can calculate ν. If you know ν, you can calculate λ. The color of visible light waves is determined by their wavelength: RED has longest λ ~700 nm (7.0 x 10-7 m) ν ~4.3 x 1014 Hz ORANGE ~620 nm (6.2 x 10-7 m) YELLOW ~580 nm (5.8 x 10-7 m) GREEN ~530 nm (5.3 x 10-7 m) BLUE ~470 nm (4.7 x 10-7 m) VIOLET has shortest λ ~420 nm (4.2 x 10-7 m) and highest ν ~7.1 x 10 14 Hz Visible light is only a small part of the entire electromagnetic spectrum: radio waves λ = 1 m to 105 m microwaves λ = 1 mm to 1 m infrared λ = 750 nm to 1 mm visible λ = 390 nm to 750 nm ultraviolet λ = 10 nm to 400 nm X-rays λ = 0.01 nm 10 nm gamma-rays λ < 0.02 nm (You are not responsible for knowing specific wavelength or frequency ranges, but you should know the relative order of colors and types of waves.) Waves have the property of superposition in phase constructive interference out-of-phase destructive interference 2 and ms ntensity of a wave = ) : cycles per second = = the tim= The # of electrons ejected was measured as a function of intensity of the incident light. These data were in direct opposition to the predictions of classical mechanics. In 1905 Einstein analyzed plots of K.E. as a function of frequency for different metals and found that all of the data fit into a linear form ν0(Rb) ν0(K) ν0(Na) Rb K Na K.E. ν y = mx + b -hν0(Rb) slope (m -hν0(K) 6.626 x 10-34 Js = Planck’s constant = y-intercept (b) = - hν0 Einstein could rewrite the equation of the line: y = mx + b -hν0(Na) K.E. = ν = frequency of incident light ν0 = threshold frequency hν = the energy of the incident light = Ei hν0 = threshold energy or workfunction (φ) Einstein postulated (1905) 1) The energy of a photon is proportional to its frequency!!! E = hν (Note Units: Joules (J) = (Js)(s-1)) 2) Light is made up of energy “packets” called “photons” 5 ) = This provided a new model for the photoelectric effect The energy of an incoming photon (Ei) must be equal to or greater than the workfunction (φ) of the metal in order to eject an electron. Any “leftover” energy is K.E. We can describe this mathematically: K.E. or Ei (Note: these are just different forms of the equation K.E = hν - hν0) Let’s try some example problems. The # of electrons ejected from the surface of a metal is proportional to the of photons absorbed by the metal and not the energy of the photons (assuming Ei ≥ φ). Thus, the intensity (I) of the light (energy/sec) is proportional to the # of photons absorbed/sec and the # of electrons emitted/ sec Unit of intensity (I High intensity means more and NOT more . Understanding that light is made up of photons (it is quantized); that the energy of a photon is proportional to its frequency; and that intensity of light is measured in photons per sec, explains the experimental observations that could not be explained by classical physics. 6 : W = ==