Answer Key for
Cosmic Abundances Activity

This activity provides practice for reading and interpreting the log plot of solar system elemental abundances.

  1. Refer to the chart of the solar system abundances
    The elemental composition of the solar system.

    From the plot, determine the abundances of the following elements:

      The abundances can be read directly from the figure, keeping in mind that the logarithm of the abundance is plotted.

    1. Hydrogen

    2. If NH represents the abundance of hydrogen, then the plots shows Log NH = 12. Inverting the logarithm gives the abundance of hydrogen as NH = 1012.

    3. Helium

    4. Likewise, Log NHe = 11, and NHe = 1011.

    5. Aluminum

    6. Log NAl = 6.5, and NAl = 3.16 x 106.

    7. Gold

    8. Log NAu = 1.0 (estimating from the plot) and NAu = 10.

    To compare the abundance of an element relative to hydrogen, take the ratio of the abundances:
    5. How much more hydrogen is there in the solar system than helium?
    To compare the abundance of helium to that of hydrogen, compute 1012/1011 = 10. So there is 10 times more hydrogen than helium. This can also be done using logarithms,
    Log (NH/NHe) = Log NH - Log NHe = 12 - 11 = 1.
    Inverting the result gives Log 1 = 101 = 10.

    6. How much more hydrogen is there than aluminum?
    Likewise, for hydrogen and aluminum, compute 1012/(3.16 x 106) = 3.16 x 105, or

    Log (NH/NAl) = Log NH - Log NAl = 12 - 6.5 = 5.5,
    There is log 5.5 = 105.5 = 3.16 x 105 times as much hydrogen as aluminum.

    7. How much more hydrogen is there than gold?
    For hydrogen and gold, compute 1012/10 = 1 x 1011, or

    Log (NH/NAu) = Log NH - Log NAl = 12 - 1 = 11,
    There is log 11 = 1 x 1011 times as much hydrogen as gold.

  2. Below is a table of the various processes in the universe that create elements. Also listed are the combined abundances (relative to hydrogen) of that particular groups of elements.

    ProcessPredominant elementsCombined
    Big Bang H, He 1.10 x 1012
    Small Stars C,N,O 1.19 x 109
    Large Stars other elements with atomic
    numbers up through Fe
    2.56 x 108
    Supernovae elements with atomic numbers
    above Fe
    1.94 x 106
    Cosmic Rays Li, Be, B 2.68 x 103

    What are ways to illustrate or plot these data?

    Because of the wide range of values, data like this are often plotted logarithmically. The Solar System abundance bar graph is an example of this. These values may likewise be plotted in a bar graph, or as a line graph, with the y-axis for the abundance plotted logarithmically.

    Another way to plot it is to add all the logarithmic values (12+9+8+6+3=38), and represent each particular process as a fraction of the total. So H and He from the big bang are 12/38=32 % of the total. A pie chart can be constructed to represent these percentages. This is what's been done along the rim of the circle on the "What is Your Cosmic Connection to the Elements?" poster.

pie chart
Pie chart representing the "logarithmic percentages" of each process.

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