Assignment Key: Electromagnetic Radiation


Planck's constant (to 3 significant figures) is 6.63x10-34J · s or 4.13x10-15eV · s
The velocity of light is 3.00x108m/s

  1. Using the relation E = hf calculate the quantum energy in joules (J) and in electron volts (eV) of a photon of an X-ray beam whose wavelength is 1.00x10-9m.
    1.99x10-16J or 1.24keV

  2. Calculate the quantum energy in joules (J) and in electron volts (eV) of a photon of a microwave beam whose wavelength is 3.00x10-2m.
    6.63x10-28J or 4.14x10-9eV

  3. A photon of exactly 10.2eV is the energy required to raise a ground state electron of a hydrogen atom to its lowest excited state. What wavelength radiation would do this? Using the Data Sheets identify as closely as possible the colour (or kind) of this radiation.
    2.47x1015Hz, which is a wavelength of 1.21x10-7m; (ultraviolet light)

  4. The binding energy of a ground state electron of a hydrogen atom is 13.6eV. Calculate the minimum wavelength of electromagnetic radiation required to knock it free i.e. to ionize a hydrogen atom. Using the Data Sheets identify as closely as possible the colour (or kind) of this radiation.
    3.29x1015Hz, which is a wavelength of 9.12x10-8m; (ultraviolet light)

  5. The binding energy of a ground state electron of a neon atom is 21.56eV. Calculate the minimum wavelength of electromagnetic radiation required to knock it free i.e. to ionize a neon atom. Using the Data Sheets identify as closely as possible the colour (or kind) of this radiation.
    5.77x1016Hz, which is a wavelength of 5.20x10-9m; (soft X-rays)

  6. The term work function refers to the minimum energy (usually in eV) required to eject free electrons from a metallic surface. Platinum has a work function of 5.32eV, one of the highest known. What wavelength of electromagnetic energy is required to eject free electrons from its surface? Using the Data Sheets identify as closely as possible the colour (or kind) of this radiation.
    1.29x1015Hz, which is a wavelength of 2.32x10-7m; (ultraviolet light)

  7. Cesium has a work function of 1.81eV, one of the lowest known. What wavelength of electromagnetic energy is required to eject free electrons from its surface? Using the Data Sheets identify as closely as possible the colour (or kind) of this radiation.
    4.38x1014Hz, which is a wavelength of 6.85x10-7m; ( red visible light)

  8. A method for measuring the work function of a metal is to attach a clean, oxide free, sheet of the metal to a leaf electroscope. One simply places a negative charge on the electroscope and then illuminates the metal with light of increasing energy (decreasing wavelength), as shown in the diagrams below, until the electroscope suddenly discharges.
    a) What is the work function of a metal if the longest wavelength that is able to discharge the electroscope (by electron emission from the top plate) is 4.36x10-7m?
    2.84eV
    b) What would you conclude if the leaves of the electroscope dropped and then began to rise (separate) after further illumination?
    The electroscope continues to eject electrons and gradually acquires a net positive charge

    Experimental Method for Determining the Work Function of a Metal
    and a Demonstration of The Photoelectric Effect


    Low Intensity, Low Energy Photons
    (No Effect)

    Transparency Master

    A negative charge is placed on an electroscope. The metal plate is then illuminated with monochromatic light of a specific wavelength.

    If the energy of the photons is below the work function of the metal, no electrons will acquire sufficient energy to break free of the metal surface.


    High Intensity, Low Energy Photons
    (No Effect)

    Transparency Master

    If the intensity of the electromagnetic radiation is increased; that is, if its brightness is increased, there is no change from the low intensity case above.

    The metal plate may experience slight warming but no electrons will be emitted.

    This is because the energy of the electromagnetic radiation acts in discrete quantum bundles called photons.

    Increasing the brightness of the light increases the number of photons (m-2·s-1) falling on the surface, but not their energy


    Low Intensity, Photon's Energy Exceeds the Work Function
    (Electrons are Ejected)

    Transparency Master

    The wavelength of the incident radiation is gradually decreased.

    Once the threshold energy of the metal's work function is reached, even the lowest intensity (faintest) light will eject electrons.

    Increasing the intensity of the light (making it brighter) increases the number of electrons ejected, but not their kinetic energy.

    For photons with energies in excess of the work function, the kinetic energy of the ejected electrons is simply the difference between the photon energy and the work function of the metal.


  9. The mass equivalent of an electron or a positron is approximately 0.511MeV. What is the minimum wavelength of electromagnetic radiation required to produce an electron-positron pair. Using the Data Sheets to identify as closely as possible the colour (or kind) of this radiation.
    Their combined energy-mass equivalent is 1.02Mev. This energy corresponds to photons of electromagnetic radiation where the associated wavelength is 1.25x10-12m; (hard X-rays)

  10. What wavelength of electromagnetic radiation would be needed to produce a particle as massive as a proton (mass equivalent 940Mev)? Using the Data Sheets identify as closely as possible the colour (or kind) of this radiation.
    This energy corresponds to photons of electromagnetic radiation where the associated wavelength is 1.32x10-15m; (high energy gamma rays)


ASSESSMENT

The chart that follows identifies four levels of achievement for assessing students' communication of information and ideas. Levels 1 and 2 describe performance that is approaching the standard for the grade; level 3 describes the standard for the grade; and level 4 describes performance that is above the standard. In numerical terms, all four levels are at passing level for the grade. Level 1 corresponds to a mark of 50%-59%; level 2, 60%-69%; level 3, 70%-79%; and level 4, 80%-100% . Student performance that is not approaching or is significantly below the standard would receive a failing grade.

Understanding of Basic Concepts

The student:

Level 1
Level 2
Level 3
Level 4
demonstrates limited understanding of how electromagnetic radiation interacts with matter by solving assignment problems with limited accuracy demonstrates some understanding of how electromagnetic radiation interacts with matter by solving assignment problems some accuracy demonstrates considerable understanding of how electromagnetic radiation interacts with matter by solving assignment problems with general accuracy demonstrates thorough understanding of how electromagnetic radiation interacts with matter by solving assignment problems with a high degree of accuracy
Inquiry

The student:

Level 1
Level 2
Level 3
Level 4
interprets and uses data relating to electromagnetic radiation with limited competence making major errors/omissions interprets and uses data relating to electromagnetic radiation with moderate competence making several minor errors/omissions interprets and uses data relating to electromagnetic radiation with considerable competence making few minor errors/omissions interprets and uses data relating to electromagnetic radiation with a high degree of competence making practically no errors/omissions
Communication of Information and Ideas

The student:

Level 1
Level 2
Level 3
Level 4
uses scientific terminology, symbols, conventions, and SI units with limited accuracy and effectiveness uses scientific terminology, symbols, conventions, and SI units with some accuracy and effectiveness uses scientific terminology, symbols, conventions, and SI units with considerable accuracy and effectiveness uses scientific terminology, symbols, conventions, and SI units with a high degree of accuracy and effectiveness


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Prepared by the YES I Can! Science Team,