Answer Key for Cosmic Abundances Activity
This activity provides practice for reading and interpreting the log plot of solar system elemental abundances.
 Refer to the chart of the solar system abundances
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.
 Hydrogen
If N_{H} represents the abundance of hydrogen, then the plots shows Log N_{H} = 12. Inverting the logarithm gives the abundance of hydrogen as N_{H} = 10^{12}.
 Helium
Likewise, Log N_{He} = 11, and N_{He} = 10^{11}.
 Aluminum
Log N_{Al} = 6.5, and N_{Al} = 3.16 x 10^{6}.
 Gold
Log N_{Au} = 1.0 (estimating from the plot) and N_{Au} = 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 10^{12}/10^{11} = 10. So there is 10 times more hydrogen than helium. This can also be done using logarithms,
Log (N_{H}/N_{He}) = Log N_{H}  Log N_{He} = 12  11 = 1.
Inverting the result gives Log 1 = 10^{1} = 10.
6. How much more hydrogen is there than aluminum?
Likewise, for hydrogen and aluminum, compute 10^{12}/(3.16 x 10^{6}) = 3.16 x 10^{5}, or
Log (N_{H}/N_{Al}) = Log N_{H}  Log N_{Al} = 12  6.5 = 5.5,
There is log 5.5 = 10^{5.5} = 3.16 x 10^{5} times as much hydrogen as aluminum.
7. How much more hydrogen is there than gold?
For hydrogen and gold, compute 10^{12}/10 = 1 x 10^{11}, or
Log (N_{H}/N_{Au}) = Log N_{H}  Log N_{Al} = 12  1 = 11,
There is log 11 = 1 x 10^{11} times as much hydrogen as
gold.
 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.
Process  Predominant elements  Combined Abundance 
Big Bang  H, He  1.10 x 10^{12} 
Small Stars  C,N,O  1.19 x 10^{9} 
Large Stars  other elements with atomic numbers up through Fe  2.56 x 10^{8} 
Supernovae elements  with atomic numbers above Fe  1.94 x 10^{6} 
Cosmic Rays  Li, Be, B  2.68 x 10^{3} 
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 yaxis 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 representing the "logarithmic percentages" of each process.

