In certain stars the carbon cvcle is more effective than the proton-proton cycle in generating energy. This carbon cycle is
$$^{12} \mathrm{C}+^{1} \mathrm{H} \rightarrow^{13} \mathrm{N}+\gamma, \quad Q_{1}=1.95 \mathrm{MeV}$$ $$
^{13} \mathrm{N} \rightarrow^{13} \mathrm{C}+\mathrm{e}^{+}+\nu, \quad Q_{2}=1.19$$$$
^{13} \mathrm{C}+^{1} \mathrm{H} \rightarrow^{14} \mathrm{N}+\gamma, \quad Q_{3}=7.55$$$$
^{14} \mathrm{N}+^{1} \mathrm{H} \rightarrow^{15} \mathrm{O}+\gamma, \quad Q_{4}=7.30$$$$
^{15} \mathrm{O} \rightarrow^{15} \mathrm{N}+\mathrm{e}^{+}+\nu, \quad Q_{5}=1.73$$$$
^{15} \mathrm{N}+^{1} \mathrm{H} \rightarrow^{12} \mathrm{C}+^{4} \mathrm{He}, \quad Q_{6}=4.97$$
(a) Show that this cycle is exactly equivalent in its overall effects to
the proton-proton cycle of Fig. $43-11$ . Verify that the two cycles, as expected, have the same $Q$ value.