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Question
Another set of reactions that result in the fusing of hydrogen into helium in the Sun and especially in hotter stars is called the carbon cycle. It is

${}^{12}\textrm{C} + {}^1\textrm{H} \rightarrow {}^{13}\textrm{N} + \gamma$

${}^{13}\textrm{N} \rightarrow {}^{13}\textrm{C}+e^+ + \nu_e$

${}^{13}\textrm{C} + {}^1\textrm{H} \rightarrow {}^{14}\textrm{N} + \gamma$

${}^{14}\textrm{N} + {}^1\textrm{H} \rightarrow {}^{15}\textrm{O} + \gamma$

${}^{15}\textrm{O} \rightarrow {}^{15}\textrm{N} + e^+ + \nu_e$

${}^{15}\textrm{N} + {}^1\textrm{H} \rightarrow {}^{12}\textrm{C} + {}^4\textrm{He}$

Write down the overall effect of hte carbon cycle (as was done for the proton-proton cycle in $2e^- + 4{}^1\textrm{H} \rightarrow {}^4\textrm{He} + 2\nu_e + 6\gamma$). Note the number of protons (${}^1\textrm{H}$) required and assume that the positrons ($e^+$) annihilate electrons to form more $\gamma$ rays.
Solution Video

# OpenStax College Physics for AP® Courses Solution, Chapter 32, Problem 36 (Problems & Exercises) (3:11) 