Unit 2: Section 1 Waves and Quantum Behaviour

Chapter 6 and 7 Advancing physics

  • Created by: R_Hall
  • Created on: 01-05-13 20:31

Superposition and Coherence

  • When two or more waves cross, the resultant displacement equals the vector sum of the individual displacements
  • Crest + crest or trough + trough is constructive interference, a bigger crest/trough is made
  • Crest+ trough is destructive interference, there is no resultant
  • Rotating arrows represent the phase of each point on a wave. Called phasors and rotate anti-clockwise in a full circle as a wave completes a full cycle
  • Two waves are in phase- both at the same point in the wave cycle. One complete wave cycle is 360° (or 2π radians)
  • If there is a phase difference of 0 or a multiple of 360°, the waves are in phase (phasors in same direction). Points of a phase difference of odd number multiples of 180° (π radians) are in antiphase (exactly out of phase) Phasors in opposite direction
  • In order to get a clear interference patter, two or more wave sources must be coherent- same wavelength and frequency, fixed phase difference
  • Whether you get constructive/destructive interference depends on path difference- the amount by which the path of one wave travels is longer that that of another wave
  • At any point at a equal distance from both sources- constructive. When path difference is a whole number of wavelengths- constructive
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Standing Waves

  • A standing  wave is the superposition of two progressive waves with the same wavelength, moving in opposite directions.
  • No energy is transmitted by a standing wave
  • Standing waves in strings form oscillating 'loops' seperated by nodes
  • Each particle vibrates at right angles to the string. Nodes are where the amplitude is 0. Antinodes are where the amplitude is maximum
  • At resonant frequencies, an exact number of 1/2 wavelengths fits onto the string
  • Longitudinal standing waves form in a wind instrument. The node will form at the closed end. Lowest resonant frequency when length of pipe= 1/4 wavelength
  • Antinodes form at open ends. If both open, lowest resonant frequency when l= 1/2 wavelength
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  • Diffraction- waves spread out as they come through a narrow gap. Gap lots bigger than wavelength= diffraction unnoticeable. Gap same size as wavelength= most diffraction
  • If gap smaller than wavelength, waves mostly reflected back
  • When a wave meets an obstacle, diffraction around edges and a 'shadow' behind object. Wider obstacle-longer shadow
  • With light waves, you get a pattern of light and dark fringes. If wavelength= size of aperture -> diffraction pattern. Bright central fringe with alternating dark/light fringes on either day. Narrower the slit, wider the diffraction pattern
  • Brightest point is where the light passes in a straight line from slit to screen. All waves are in phase
  • All other bright points, constant phase difference, so the phasors all point in a slightly different direction- smaller resultant
  • Dark fringes are where the phase difference between waves mean phasors add up to form a circle, 0 resultant
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Two-Source Interference

  • For two-source interference to occur, you need coherent sources (same wavelength and frequency). Easy with sound and water, but hard with light-
  • A single laser light is shone through two slits, as it is coherent and monochromatic
  • Slits have to be same size as wavelength of laser light so it is diffracted. Light from the slits acts as two coherent point sources
  • Pattern of dark and light fringes depending whether constructive or destructive interference. 
  • Thomas Young came up with an equation to work out wavelength of light from this experiment- Young's double-slit formula
  • The fringes are so small that it's hard to get an accurate value of X. Measure across several fringes and divide by number of fringe widths between them
  • Newton suggested light was made up of particles called 'corpuscles'. Explained reflection and refraction, but only waves (as put forward by Huygens) can show diffraction and interference
  • Young's double slits confirmed Huygen's wave theory- light can diffract (through narrow slits) and interfere (form interference pattern)
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Diffraction Gratings

  • When you diffract through more slits, the patterns get sharper. Bright bands are brighter and dark bands are darker. Sharper fringes make for more accurate measurements
  • For monochromatic light, there is a line of maximum brightness at the centre- zero order line. The lines either side are the 1st order, and the next pair are the 2nd order
  • The larger the wavelength, the more the pattern will spread out. 
  • The coarser the grating, the less the pattern will spread out
  • White light is a mixture of colours. If diffracted, the patterns due to different wavelengths within the white light spread out by different amounts
  • Each order becomes a spectrum. 0 order stays white as all the wavelengths just pass through
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Light and Photons

  • Light travels very fast, makes speed of light hard to measure.
  • The photoelectric effect can only be explained if light acts as a particle- a photon
  • If light of high frequency is shone onto the surface of a metal, it will emit electrons. Free electrons on the surface absorb energy and vibrate, and eventually the bonds holding it to the metal break and the electron (photoelectron) is released
  • No electrons are emitted below a certain frequency- threshold frequency. Electrons have different KE's, value of maximum KE increases with frequency of radiation, not intensity. Number of electrons emitted per s proportional to intensity
  • Einstein suggested than EM waves can only be released in discrete packets- quanta, and that they can only exist in discrete packets called photons
  • Higher the frequency, more energy carried
  • He believed photons act as particles, will either transfer all or none of its energy
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Energy Levels and Photon Emission

  • Electrons in an atom can only exist in certain defined energy levels. Each level has a number, n=1 is ground level. Electrons can move down a level by emitting a photon
  • Since transitions are between definite energy levels, the energy of each photon emitted can only take a certain value. Energy carried by each photon= difference in energies between two levels
  • If a gas is heated, electrons move to a higher energy levels before falling back down, emitting energy as photons
  • If the light from a hot gas is split (with prism or diffraction grating) get a line spectrum (bright lines on black background). Each line corresponds to the wavelength of emitted light
  • The spectrum of white light is continuous, there are no gaps in the spectrum. Hot things emit a continuous spectrum in the visible and infrared
  • Line absorption spectrum- light with a continuous spectrum passed though cool gas. A low temps, most electrons will be in ground state. Photons of correct wavelength are absorbed by electron to promote to high energy levels
  • See a spectrum with black line corresponding to absorbed wavelengths
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The 'Sum Over Paths' Theory

  • Feynman believed that a photon will explore all possible paths from source to detector in one go. This can be mapped using phasors
  • In quantum mechanics, phasors are used to see how probable it is for a quantum to arrive in a particular place. 
  • As a phasor travels, it will rotate anti-clockwise until it reaches the detector. Using the energy and Planck's constant, frequency can be calculated
  • As there are an infinite number of phasors, only calculate the straightest/quickest possible paths
  • You can find the probability that a quantum will arrive at a point by squaring the resultant phasor amplitude
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Using 'Sum Over Paths'

  • When you reflect a photon off a mirror, it will explore every possible path. By finding the phasors for each path, you can find the final resultant
  • The phasore nearest the quickest path have phasors that almost line up, giving the most amplitude of the resultant, so the most probability that the photon will reach the detector
  • The phasors for longer, slower paths curl up to cancel themselves out- adding almost nothing to the resultant
  • The final phasor of the quickest path will contribute the most to the resultant amplitude and the probability of a quantum arriving at a point
  • This explains why light travels in a straight line- shortest and quickest path
  • When light travels in water, it slows down, but frequency is constant. The photons still have the same energy, the phasor will have the same amplitude and frequency despite material
  • To focus photons, you need to make sure all straight line paths from source to focus point take the same amount of time
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Quantum Behaviour of Electrons

  • The de Broglie equation relates a wave property to a moving particle property
  • Diffraction patterns are observed when accelerated electrons in a vacuum tube interact with the spaces in a graphite crystal. As an electron hits a fluorescent screen, it causes a photon to be released. Using phasors, the higher the probability, the brighter the point. 
  • This confirms electrons show quantum behaviour
  • Increase the electron speed and the diffraction pattern circles squash together towards the middle
  • You only get a diffraction if a particle interacts with an object about the same size as its de Broglie wavelength
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يوجد أنواع عديدة من المبيدات التي يمكن استخدامها لمحاربة الصراصير، منها ما هو على شكل طعوم، والبعض الآخر يكون بشكل سائل، يتم توزيعها على المناطق التي تتواجد فيها الصراصير في المطبخ، كمنطقة خلف الثلاجة، وتحتها، وفي خزائن المطبخ وزواياها، وخلف الغسالة، فتأتي الصراصير لحمل الطعم إلى أعشاشها، مما يتسبب بإصابة بقية الحشرات الأخرى وبيوضها، وبالتالي القضاء عليها بالكامل، مع العلم أن هذه الأنواع من المبيدات يمكن أن يستمر تأثيرها في القضاء على الصراصير لمدة ثلاثة أشهر بعد الاستخدام، ويجب مراعاة توزيعها في أماكن بعيدة عن الأطفال، والحيوانات الأليفة الموجودة في المنزل، لأنها يمكن أن تشكل خطراً عليها

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