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9.4 From ideas to implementation: 2. The photoelectric effect and black body radiation

Syllabus reference (October 2002 version)
2. The reconceptualisation of the model of light led to an understanding of the photoelectric effect and black body radiation	Students learn to: describe Hertz's observation of the effect of a radio wave on a receiver and the photoelectric effect he produced but failed to investigate outline qualitatively Hertz's experiments in measuring the speed of radio waves and how they relate to light waves identify Planck's hypothesis that radiation emitted and absorbed by the walls of a black body cavity is quantised identify Einstein's contribution to quantum theory and its relation to black body radiation explain the particle model of light in terms of photons with particular energy and frequency identify the relationships between photon energy, frequency, speed of light and wavelength: and	Students: perform an investigation to demonstrate the production and reception of radio waves identify data sources, gather, process and analyse information and use available evidence to assess Einstein's contribution to quantum theory and its relation to black body radiation identify data sources, gather, process and present information to summarise the use of the photoelectric effect in photocells solve problems and analyse information using: and process information to discuss Einstein and Planck's differing views about whether science research is removed from social and political forces

Extract from Physics Stage 6 Syllabus (Amended October 2002). © Board of Studies, NSW.
[Edit: 14 Aug 08]

Prior learning: Preliminary module 8.2 (subsections 1, 3 and 4)

perform an investigation to demonstrate the production and reception of radio waves

• Perform the investigation by selecting a procedure like that described below and carrying it out, recognising where and when modifications are needed and analysing the effect of any adjustments that you make. Write an account to explain how this investigation demonstrates the production and reception of radio waves. Note particularly any scientific controls that help you demonstrate this.

describe Hertz's observation of the effect of a radio wave on a receiver and the photoelectric effect he produced but failed to investigate

• Hertz observed that the spark between the gap in the transmitter loop caused an electrical disturbance between the gaps in the detecting loop.
  
  
• Hertz observed that the gap in the detector could be made larger and still generate sparks when the radiation from the transmitting spark shone directly into the gap in the detecting loop. Hertz did not recognise that the UV component in the transmitter spark removed free electrons from the surface of the metal, thus allowing the discharge (spark) to occur across a wider gap.

outline qualitatively Hertz's experiments in measuring the speed of radio waves and how they relate to light waves

• In 1887 Hertz produced experimental evidence for the existence of electromagnetic waves, theoretically predicted by Maxwell in 1864.
  
  
• Hertz set up an induction coil. As sparks were generated across a small gap they induced sparks in a detecting loop a small distance away. This spark was evidence for electromagnetic waves travelling through space from the induction coil to the detecting loop.
  
  
  
  
• Hertz was able to calculate the velocity of the waves by reflecting the generated waves off a metal sheet and measuring the wavelength of the standing wave set up by interference. Substituting this wavelength and the known frequency of the wave generator into the general wave equation, v = λ x f, Hertz calculated the wave speed at 3 x 10⁸ ms^-1, very close to the values for the speed of light earlier estimated by Maxwell and measured by Fizeau.

identify Planck's hypothesis that radiation emitted and absorbed by the walls of a black body cavity is quantised

Background information
It was thought that the energy absorbed and emitted by a black body should be continuous, that is, could occur in any amount, and should increase as the wavelength became shorter. This was not supported by the experimental data as shown in the sketch. The amount of energy radiated reaches a maximum at a wavelength that depends on the temperature of the black body.

• Planck's explanation for the observations involved the radical idea that energy could only be radiated or absorbed in small discrete amounts, later called quanta, now identified as photons. The size of each quantum of energy is characteristic of the frequency of light emitted.

identify data sources, gather, process and analyse information and use available evidence to assess Einstein's contribution to quantum theory and its relation to black body radiation

This investigation can be conducted by gathering a range of resources including scientific journals, CD-ROM resources and the Internet.

• In deciding the type of data necessary for this investigation, you need to:
  • consider the type of information about quanta and black body radiation that needs to be collected
  • select data sources.
  
  
• To process the information in the sources you find, assess its reliability by comparing the information provided. Look for consistency of information.
  
  
• Analyse the information to make a generalisation regarding Einstein's use of quantum ideas to explain the properties of black body radiation.

identify Einstein's contribution to quantum theory and its relation to black body radiation

• Einstein explained Planck's work in the following way:
  
  The energy associated with the radiation from a black body is concentrated in packets of energy called photons. A photon is the smallest amount of radiation energy possible at a particular frequency. A photon cannot transfer part of its energy: it can only transfer all of its energy or none of it. The amount of energy carried by a photon is proportional to its frequency. The intensity of light is proportional to the number of photons. The energy possessed by a photon is proportional to its frequency, hence the observation, in relation to black body radiation, that the shorter the wavelength (thus the higher the frequency) the greater the total energy radiated (for a given temperature).
  
  
• Einstein also explained that wave and particle behaviour can coexist.

explain the particle model of light in terms of photons with particular energy and frequency

• Some of the properties of light are best explained if light is considered to consist of a stream of particles, or discrete bundles of energy, called photons.
  
  
• A photon carries an amount of energy that is proportional to the frequency of the radiation (light). All photons of light of a particular frequency have precisely the same amount of energy. The higher the frequency of the light, the more energy the photon possesses, thus photons of ultraviolet light have higher energy than those of blue light, which in turn have higher energy than photons of red light.
  
  
• All photons, regardless of their frequency, have zero rest mass and travel at 3 x 10⁸ m s^-1 in a vacuum.

identify data sources, gather, and present information to summarise the use of the photoelectric effect in photocells

• Decide what data you need to gather and in what form you will gather it so that it can be efficiently processed. It might be useful to work with a group to collect information to produce a set of annotated diagrams. You will need to decide on the format of the diagrams and the language to be used.
  
  
• Try to gather information from a range of resources, including popular scientific journals, digital technologies like CD-ROMs and the Internet. Focus on collecting explanations of how the function of each device depends on the photoelectric effect.
  
  
• Present the information to other students. You may use visual aids such as overhead transparency graphics or a Power Point presentation. Keep the information simple with just the summary asked for in the syllabus point.
  
  
• Your summary could include a brief statement on some or all of the following:
  • How are the design and construction of the device related to its photoelectric function?
  • How are the output voltage and/or current related to the intensity and/or the frequency of incident light?
  • What industrial, scientific, commercial or domestic technologies use this device?
  • What are the advantages or limitations of the device?

identify the relationships between photon energy, frequency, speed of light and wavelength:

and

• The energy of a photon is given by the relationship E = h x f, where:
  • E is the energy of the photon in joules (or electron volts)
  • h is Plank's constant: 6.6 X 10^-34 J s
  • f is the frequency of the light in hertz (seconds^-1).
  
  
  
• The speed of light is given by the relationship , where
  • c is the speed of light: 3 x 10⁸ m s^-1
  • f is the frequency of the wave
  •  is the wavelength of the wave.
    
    
• By combining the two equations,

solve problems and analyse information using: and

• Solve problems by selecting the appropriate equation, rearranging the equation where necessary, substituting known data for the variables, and computing the answer.
  
  A sample problem:
  
  Calculate the wavelength and the energy of a photon of light with frequency equal to 1.984 x 10¹⁴ Hz.
  
  Calculating the wavelength, from :
  
  Calculating the energy of the photon:
  
  
• Analyse information by examining relationships between the variables in the equations given.
  
  Sample analysis question:
  
  Two of the lines in the emission spectrum of mercury represent violet light of wavelength 4.05 x 10^-9 m and red light of wavelength 6.90 x 10^-9 m. Which of these wavelengths would have the more energetic photons?
  
  Answer:
  
  Photons of the violet light would have more energy. From the wave equation c = f x λ we can see that, as violet light has a shorter wavelength than red light, its frequency is higher. From Planck's equation E = h x f, therefore the energy of violet photons is greater than the energy of red photons.

process information to discuss Einstein and Planck's differing views about whether science research is removed from social and political forces

• Gather information by looking in encyclopaedias, scientific and popular journals, magazines and text books, as well as searching the Internet and CD–ROMs such as Encarta or Encyclopaedia Britannica. Use search strings such as “Political views of Albert Einstein” and “Life of Max Planck”.
  
  
• Process your information by assessing its relevance to your topic and assessing its reliability by comparing information from various sources.
  
  
• Summarise your information to describe the social and political influences on both Einstein and Planck at the time, and to describe the views held and actions taken by each of them.

This is a website about the science more than the philosophy but it is worth having a look at. On Truth and Reality

References

Heilbron, J., 2000, The dilemmas of an upright man. Max Planck and the fortunes of German science. With a new afterword. Cambridge (MA), London. This biography of Planck lays out the two sides of the issue.

Rosenthal-Schneider, I., 1980, Reality and scientific truth. Wayne State University Press, Detroit, ISBN 0-81-431650-6. This is an engaging collection of essays about and correspondence with Einstein, Planck and von Laue, by Ilse Rosenthal-Schneider, who was taught by these three in Germany before she emigrated to Australia. She spent the second half of her life at the University of Sydney, where she taught the history and philosophy of science.

Walker, M., 1995, Nazi science: Myth, truth and the German atomic bomb. Plenum, New York, ISBN 0-306-44941-2.

American Institute of Physics (AIP), June 2001, Albert Einstein: image and impact, in Public concerns American Institute of Physics web site, USA. The following is a relevant quotation from their AIP web site: