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Light and other electromagnetic radiation Goals--we want to understand: 1. the bizarre, dual nature of light 2. the structure of atoms 3. how we use light to gain information on objects that we cannot touch 4. what determines how bright an object actually is and how bright it appears to us Just what IS light, anyway? Does it consist of waves of electromagnetic energy? (Huygens) -orDoes it consist of particles (photons)? (Newton) -YES- You can devise an experiment that will prove conclusively that either of the above cases is true. • When light propagates, it is best described as a wave. • When light interacts with matter, it is best described as photons. This is the clearest example of a concept in quantum mechanics called wave-particle duality. • On small scales, all things show some behaviour that is “wavelike,” and some that is “particle-like.” Light as a wave A light wave consists of an electric field, and a magnetic field, both of which are oscillating. • As the electric field changes, it causes the magnetic field to change, and vice-versa. • This way, electromagnetic waves are able to propagate through space all by themselves. – Other waves need some medium through which they can propagate (sounds waves through air, for example). If we draw only the electric field, then the light wave looks more familiar: Wavelength, λ We describe waves by their: •Wavelength (λ): The distance between identical points on the wave. •Frequency (f): The number of wavelengths that pass by each second. Wavelength and frequency are related by: λf = c C = speed of light. The same for all electromagnetic waves. Question: A difference between electromagnetic waves and either sound or water waves is: a) Electromagnetic waves all have shorter wavelengths. b) Electromagnetic waves can travel in a vacuum. c) Electromagnetic waves all have the same amplitude. d) Electromagnetic waves can travel from place to place instantaneously. Units: Wavelength: • Angstrom (Å): 10-10 meters • Nanometers (nm): 10-9 meters • Microns (µm): 10-6 meters • Millimeters (mm): 10-3 meters • Meters (m): about three feet Frequency: • Hertz: 1 cycle per second • Megahertz (MHz): 106 cycles per second • Kilohertz (kHz): 103 cycles per second Our eyes are sensitive to a very small part of the electromagnetic spectrum. Name: Typical wavelengths Frequencies X-rays < 10 Å > 3x1017 Hz Ultraviolet (sunburn) 30-3000 Å 9x1014-1017 Hz Visible light 4000-8000 Å Infrared (heat) 1-100 µm 4-8x1014 Hz 3x1012-3x1014 Hz 100 µm - few mm about 3x1011 Hz FM Radio 2.8 - 3.4 m 88 - 108 MHz AM Radio 188 - 556 m 540 - 1600 kHz Microwaves Diffraction and interference are explained if light is a wave: the twoslit experiment shows both of these at work. Bright lines are seen on the screen where the difference in the path lengths from the two slits to the screen is an integer number of wavelengths. Dark lines are seen where the difference is an odd half number of wavelengths. Incoming parallel wave crests Screen with two slits Viewing screen When the paths from the two slits to the screen differ by λ, 2λ…, the two waves add. This is called constructive interference. + = When the path are l/2, 3l/2… different, the waves cancel. This is called destructive interference. + = Doppler Shift The change in the observed color of light because the source and the observer are either approaching or moving away from each other. Static light source: color looks the same to all observers. Circles are crests of waves moving away from light source Moving light source: light waves expand around where the source was when they were emitted. 1 1 2 1 2 3 Sees a redshift Sees a blueshift Sees no shift Question: In which of the following situations would the light that we see from a star show a blueshift? a) The star is moving away from us. b) The star is moving across our field of view. c) The star is moving towards us. Light as particles We also think of light as coming in discrete particles, called photons. • Each photon has a wavelength associated with it, the same as the wavelength of the color light it represents. • Each photon has an energy given by its wavelength (or, equivalently, its frequency) as: E = hf This view of light was introduced by Einstein to explain the photoelectric effect. electrons photons metal Types of Spectra • • • Continuous spectrum – All colors present to some degree. – From a hot solid, liquid, or very dense gas. Emission-line spectrum – Only light at certain, very specific wavelengths is present. – From a hot gas. Absorption-line spectrum – All colors are present, except at certain wavelengths. – From a cool gas in front of a continuous source. Continuous Spectra Most sources of continuous spectra emit Planck (or “blackbody”) spectra. energy wavelength The wavelength where the spectrum peaks depends upon the temperature of the source, according to Wien’s Law. λ peak 1 ∝ T The total amount of electromagnetic energy emitted by a continuous source increases very rapidly with its temperature, as described by Stefan’s Law. F∝Τ • • • 4 F is the flux. It is the amount of energy emitted by every unit area of the surface of the light source. For example, a star that is twice as hot as the Sun (but the same size) would be 16 times brighter. Because of this, it is the rare hot stars that dominate the light that we see from most galaxies. By looking at continuous spectra from multiple sources, we see both Stefan’s and Wien’s Laws in action The total amount of light emitted by an object (the luminosity) also increases with the total amount of emitting area. For a star, this means that: 2 source L∝R • • R is the radius of the emitting object (NOT the distance to it). A star with twice the radius of the Sun (but the same temperature) would emit four times more light. € Questions: Two stars have the same radii. One is blue and the other is red. The red star appears to be twice as bright as the blue star when you see them in the sky. Which star is emitting more light? a) The red star. b) The blue star Which star is hotter? a) The red star. b) The blue star. Which star is further away? a) The red star. b) The blue star. Emission and Absorption Spectra “Fingerprints of the atoms” We can think of atoms as looking like miniature Solar Systems. One or more negatively-charged electrons orbit around a nucleus that consists of positively-charged protons and neutral neutrons. + ordinary hydrogen + deuterium 0 - - + 0 - 0 + helium - Unlike the Solar System, the electrons can only exist in certain orbits, called energy levels. Higher energy + - The lowest possible energy level, where the electron likes to be, is called the ground state. When a photon of the right energy hits an atom, the electron can use the energy of the photon to move to a higher energy level. The photon is absorbed in the process, resulting in an absorption-line spectrum. before after Wrong energy Right energy In reverse, an electron that is in a high energy level will spontaneously “jump” to a lower level. The energy that it loses is emitted as a photon. The result is an emission-line spectrum. before after The atoms of each element have unique arrangements of energy levels, and so each elements has a unique absorption and emission-line spectrum. By examining an absorption or emission-line spectrum, we can therefore determine the chemical makeup of the emitting object. Another inverse-square law The apparent brightness of an object (a star, a candle, a flashlight…) decreases with the square of distance, like gravity. Imagine two spheres centered on a light source. The same photons pass through both spheres. The area of a sphere: A = 4πR 2 R1 R2 The apparent brightness is total light 1 ∝ 2 area R This means, for example, that sunlight is 900 times fainter at Neptune than at Earth. Question: Which of the following characteristics of light are associated with the wave nature of light? a) Constructive interference and diffraction. b) The Doppler effect and the formation of spectral lines. c) Formation of spectral lines and the photoelectric effect. d) Diffraction and the photoelectric effect.