Homework 10. Advanced Nuclear Burning

Consider a star which starts out with a mass of 20.0 M of pure hydrogen (H). (Note: this initial composition and some of the subsequent reactions have been simplified for this question!) By the end of its life, the star has the structure shown in the diagram at right, with an iron (Fe) core of 1.4 M, surrounded by 0.6 M of sulfur (S), 1.5 M of oxygen (O), 2.5 M of helium (He), and 14.0 M of unburned hydrogen.

1. During the star's entire lifetime, how much helium was produced in nuclear reactions (including helium which has since been burned in other reactions)? Give your answer in units of solar mass (M). 2. How much oxygen was produced in nuclear reactions (again, including oxygen burned subsequently)? 3. How much sulfer was produced in nuclear reactions (again, including sulfer burned subsequently)? 4. How much iron was produced in nuclear reactions?

At each stage of nuclear burning, a tiny fraction of the mass is converted to energy. The table below lists the fractions converted at each of the nuclear reactions taking place in this star.

For example, when   1 M   of iron is produced by the reaction   2S -> Fe  , just   1 M × 0.00030 = 0.00030 M   of mass is converted to energy. (These fractions are small enough that I've ignored them in describing the star's final structure; that's why the final mass adds up to exactly 20.0 M).

5. During the star's life, how much mass was converted to energy by the reaction   2S -> Fe   ?

6. How much mass was converted to energy by the reaction   2O -> S   ?

7. How much mass was converted to energy by the reaction   4He -> O   ?

8. How much mass was converted to energy by the reaction   4H -> He   ?

9. Finally, when the iron core collapses, gravity converts   0.2 M   of` mass to energy. How does this compare to the total amount of mass converted to energy by nuclear reactions?

Joshua E. Barnes (barnes@ifa.hawaii.edu) Last modified: October 30, 2006 http://www.ifa.hawaii.edu/~barnes/ast110_06/homework/hw10.html