Assignment Key: Natural Sources of Electromagnetic Radiation

  1. The solar constant is defined as the total radiant power of the Sun, per square metre, received at the Earth's orbit (outside of the Earth's atmosphere).

    a) You must treat the illuminated face of the Earth as if it were a disk, not a hemisphere, when calculating the total area of sunlight falling on the Earth's surface. Can you explain why?
    The Earth' shadow is a circular disk, i.e a disk of energy is intercepted by the Earth.

    b) Using the radius of the Earth, and the solar constant, calculate the total radiant power incident on the Earth's sunlight surface.
    1.74x1017W or 174 million billion watts

  2. In order for the Earth to remain (on average) in thermodynamic equilibrium, how much electromagnetic power must the Earth radiate into space?
    The Earth must radiate 1.74x1017W into space, otherwise it would gradually get warmer or cooler until equilibrium was established.

  3. Given that, on average, the Earth radiates electromagnetic energy uniformly from its entire surface, what is the global average power (W·m-2) emitted per square metre of the Earth's surface?
    (Surface area of a sphere 4(3.14)r2)
    3.40x102W·m-2

  4. a) Using the Stefan-Boltzmann law, Epower = 5.79x10-8T4 calculate the equilibrium temperature of the Earth using your results from question (3) above.
    277K

    b) Compare this to the current value of approximately 290K. Can you account for the difference?
    The Earth's atmosphere is slightly opaque to infrared radiation and this creates a greenhouse effect, maintaining the Earth at a habitable temperature. In this example we have ignored the fact that 30% of Sun's energy is reflected back into space. The Earth's equilibrium temperature is actually well below 250K without the green-house effect of its atmosphere.

  5. The Universe is bathed in weak microwave radiation which appears isotropic and constant. Its spectrum resembles that of a perfect black-body whose electromagnetic spectrum peaks at
    9.66x10-4m. This is the cosmic microwave background which was predicted by George Gamow in 1948. Using Wien's Displacement Law () calculate the temperature of this background radiation.
    3K

  6. Einstein's famous equation (which solved the perplexing photo-emission dilemma) is given as,
    E= hf
    Using this equation calculate the frequency and the wavelength of a 4.5MeV gamma ray from the alpha decay of radium 88Ra226.
    1.09x1021Hz; 2.7x10-13m

  7. Calculate the frequency and the wavelength of a 185.7keV gamma ray from the alpha decay of radon 86Rn222.
    4.50x1017Hz; 6.67x10-10m
The solar constant - Csolar = 1.36x103 W·m-2
The velocity of light - c = 3.00x108m/s
Distance to the Sun - 1A.U. = 1.50x1011m
Radius of the Earth - re = 6.38x106m
Planck's constant (to 3 significant figures) is h = 6.63x10-34J · s or 4.13x10-15eV · s

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 natural sources of electromagnetic radiation by solving assignment problems with limited accuracy demonstrates some understanding of natural sources of electromagnetic radiation by solving assignment problems some accuracy demonstrates considerable understanding of natural sources of electromagnetic radiation by solving assignment problems with general accuracy demonstrates thorough understanding of natural sources of electromagnetic radiation by solving assignment problems with a high degree of accuracy
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,