= Solution
\b[The elements have several complementary origins: primordial light nuclei, stellar and explosive fusion products, and nuclei built by neutron capture. Chemical enrichment also requires their ejection, rather than merely their production inside a star.] <Nucleosynthesis> and transport into the <interstellar medium> must therefore be considered together.
<Hydrogen> and much of the <helium> are primordial. During <Big Bang nucleosynthesis>, a cooling, expanding plasma assembled surviving <neutrons> and <protons> into <deuterium>, helium-3 and especially helium-4, with small abundances of lithium-7 or its beryllium-7 progenitor. Unstable nuclei at mass numbers five and eight, together with the rapidly falling density and short available time, obstructed sustained production of heavier nuclei. The <carbon>, <oxygen> and heavier material in later generations consequently require other sites. <Cosmic rays> fragment heavier interstellar nuclei and contribute importantly to the light elements lithium, beryllium and boron, which ordinary stellar burning tends to destroy.
\b[Burning stages depend on initial stellar mass.] <Stellar nuclear fusion> can release energy when the products have greater <nuclear binding energy> than the reactants. The resulting <stellar thermostat> links nuclear burning to <hydrostatic equilibrium>: when fuel exhaustion lowers heating, contraction raises the central <temperature> until another fuel can ignite, if the core becomes hot enough. Higher nuclear charges bring larger <Coulomb barriers>, so later charged-particle burning generally requires progressively higher <temperatures>. Whether the core reaches them depends on its mass, <electron degeneracy pressure>, mixing and envelope loss.
An approximately solar-composition $1M_\odot$ star first spends most of its life on the <main sequence>, converting <hydrogen> into <helium> mainly through the <proton–proton chain>. The net conversion is four protons into one helium-4 nucleus, with positrons and <neutrinos>; the small <CNO cycle> contribution redistributes CNO catalyst abundances but is not a net source of carbon at this stage. Exhaustion of central <hydrogen> leaves a helium-rich core. A surrounding <hydrogen-burning shell> continues to add <helium>, while the core contracts and the envelope expands into a <red giant>.
The low-mass helium core becomes supported substantially by <electron degeneracy pressure>. At roughly $10^8\,\mathrm K$, the <Triple-alpha process> ignites, first making transient beryllium-8 and then carbon-12 through the <Hoyle state>. Because degeneracy initially weakens the usual expansion response, this ignition is a <helium flash>. It heats and lifts the degeneracy of the core, leading to a stable phase of <core helium burning>. The <Triple-alpha process> makes <carbon>; competing <carbon-12 alpha capture> makes <oxygen>:
$$
3\,{}^4\mathrm{He}\longrightarrow{}^{12}\mathrm C,\qquad
{}^{12}\mathrm C(\alpha,\gamma){}^{16}\mathrm O.
$$
After central <helium> exhaustion, the star develops a carbon-oxygen core, a <helium-burning shell> and a more external <hydrogen-burning shell>. On the <Asymptotic giant branch>, recurrent <thermal pulses of an asymptotic-giant-branch star> arise from unstable helium-shell burning. <Stellar dredge-up> can bring processed material toward the surface, with its efficiency depending on mass and composition. The eventual <stellar wind> removes the envelope; the hot exposed core can illuminate a <planetary nebula>, and the remnant becomes a <carbon-oxygen white dwarf>. A usual isolated $1M_\odot$ star does not ignite <carbon burning>. In particular, an element synthesized in its core need not all escape: much of the carbon and oxygen remains locked in the <white dwarf>.
An approximately $5M_\odot$ star burns central <hydrogen> predominantly through the <CNO cycle>, usually in a convective core. The CNO nuclei act as catalysts; the slow nitrogen-14 proton-capture step tends to accumulate nitrogen-14 while converting <hydrogen> into <helium>. After central fuel exhaustion, a <hydrogen-burning shell> surrounds the contracting helium core. Unlike the $1M_\odot$ case, <core helium burning> normally begins before strong electron degeneracy, without a classical <helium flash>. The same <Triple-alpha process> and <carbon-12 alpha capture> create a carbon-oxygen core.
The $5M_\odot$ star then enters the <Asymptotic giant branch>, with hydrogen and helium burning in shells. Repeated thermal pulses and <stellar dredge-up> can enrich its envelope with freshly made <carbon> and <s-process> nuclei. <Hot-bottom burning> can occur when the base of the convective envelope is sufficiently hot: the <CNO cycle> processes dredged-up carbon into <nitrogen>, so a massive AGB star need not become carbon-rich despite making carbon below its envelope. Helium-shell reactions on neon-22 can also provide neutrons for the <s-process>. For an ordinary $5M_\odot$ model, strong envelope loss generally precedes carbon ignition, leaving a <carbon-oxygen white dwarf>. The exact threshold for carbon ignition and the size of these yields depend on <metallicity>, mass loss and mixing; they are not universal integers fixed solely by initial mass.
A $20M_\odot$ star reaches much more advanced stages. It starts with convective-core <CNO cycle> <hydrogen burning>, followed by <core helium burning>. After central <helium> exhaustion, contraction can ignite <carbon burning> at temperatures approaching $10^9\,\mathrm K$. Carbon-fusion channels make products including <neon>, <sodium> and <magnesium>. <Neon burning> then uses <photodisintegration> of neon-20 to release oxygen-16 and an <alpha particle>, followed by capture of that alpha particle on another neon-20 nucleus; the combined network releases energy and produces magnesium-24. <Oxygen burning> makes silicon-group nuclei through channels such as
$$
{}^{16}\mathrm O+{}^{16}\mathrm O\longrightarrow{}^{28}\mathrm{Si}+\alpha.
$$
At still higher <temperature>, <silicon burning> rearranges nuclei by <photodisintegration> and captures of protons, neutrons and <alpha particles>. It is not principally direct fusion of two silicon nuclei. Networks approach quasi-equilibrium and then <nuclear statistical equilibrium>, producing an iron-group core whose precise mixture depends on the <electron fraction in stellar matter>. Outer shells retain different stages of burning, giving an approximately layered structure. Increasing <stellar neutrino energy loss> makes advanced burning stages much shorter than <hydrogen burning>.
Near the iron group, <nuclear binding energy> per nucleon is close to its maximum. Further fusion cannot provide the sustained energy source required to support the core. As the core grows, <electron capture> reduces electron-pressure support and <photodisintegration> absorbs energy, assisting gravitational collapse. A successful <core-collapse supernova> ejects some of the envelope and processed shells, and leaves a <neutron star> or <black hole>. The shock also causes explosive burning, changing the pre-existing abundances. A $20M_\odot$ initial mass does not uniquely fix the explosion or remnant: envelope loss, rotation, composition and fallback all matter, and some collapses fail to eject much material.
\b[Ejection determines the enrichment of the interstellar medium.] Low- and intermediate-mass stars return <helium>, CNO-processed matter, dredged-up <carbon> and <s-process> products through <stellar winds> and envelope expulsion. Massive-star winds can expose hydrogen- or helium-burning products before collapse. Successful <core-collapse supernovae> eject substantial oxygen and other alpha-capture products, together with some iron-group matter formed in hydrostatic and explosive burning. Material that falls back or remains in a <stellar remnant> is withheld from the <interstellar medium>. Subsequent mixing, cooling and star formation distribute the escaped material into new stars. The distinction between production and ejection is why an internal burning inventory alone is not a stellar yield.
<Binary stars> provide an additional major iron-group source. In a <Type Ia supernova>, a carbon-oxygen <white dwarf> in a binary undergoes thermonuclear disruption after an appropriate accretion or merger history. Explosive carbon and oxygen burning makes intermediate-mass and iron-group nuclei. Much initially synthesized nickel-56 decays through cobalt-56 into iron-56; this <radioactive decay> also powers the <supernova> light curve. Such explosions have delay times and yields different from those of massive-star collapse, and help explain why iron enrichment need not track oxygen enrichment exactly.
\b[Neutron capture builds much of the material beyond iron.] Charged-particle reactions encounter increasing <Coulomb barriers> as nuclear charge grows, but a neutral <neutron> does not encounter that barrier. <Neutron capture> raises mass number, and subsequent <beta-minus decay> can turn a neutron into a proton and raise atomic number. The relative capture and decay times select different paths through the nuclear chart.
In the <slow neutron-capture process>, most unstable intermediates decay before the next capture, so the path stays near stable nuclei. In <Asymptotic giant branch> stars, important neutron sources are
$$
{}^{13}\mathrm C(\alpha,n){}^{16}\mathrm O,\qquad
{}^{22}\mathrm{Ne}(\alpha,n){}^{25}\mathrm{Mg}.
$$
The carbon-13 source operates in suitable partially mixed layers, while the hotter helium-shell pulses can activate the neon-22 source. Captures on pre-existing seed nuclei produce elements such as strontium and barium and, under suitable conditions, lead. <Stellar dredge-up> and <stellar winds> return these products to the <interstellar medium>. Massive stars also have a weak <s-process>, notably using neon-22 during helium- and carbon-burning phases; it need not produce the same abundance range as the main AGB contribution.
In the <rapid neutron-capture process>, very high neutron densities permit many captures before typical <beta-minus decays>. The path moves to neutron-rich nuclei, which later decay toward stability, producing heavy nuclei including lanthanides and actinides. Neutron-rich ejecta from <neutron star mergers> provide an established site: a merger can eject dynamical material and disk outflows, and <radioactive decay> of the newly made nuclei powers a <kilonova>. Special neutron-rich outflows associated with some massive-star collapses are additional candidate sites. It would be unjustified to assume that every ordinary <core-collapse supernova> produces the full heavy <r-process> pattern; the required neutron richness and expansion history are restrictive.
The two neutron-capture processes do not make every isotope beyond iron. Some proton-rich isotopes bypass their main paths. <Gamma-process nucleosynthesis>, for example, uses <photodisintegration> of pre-existing heavy seed nuclei in hot explosive material. Other proton-rich reaction paths can matter in suitable environments. Thus “heavier than iron” describes a family of production mechanisms rather than a single further ordinary fusion stage.
\b[Binaries change both stellar evolution and the delivery of elements.] <Roche-lobe overflow>, wind transfer and mergers can strip a donor, rejuvenate a <mass-gaining star>, alter core and envelope masses, and change the timing and character of an eventual explosion. Binary stripping can remove the hydrogen envelope of a massive <core-collapse supernova> progenitor. Accretion onto a <white dwarf> can cause a <classical nova>, ejecting hydrogen-burning products and particular isotopes while ordinarily leaving the <white dwarf> intact; this differs from the destructive <Type Ia supernova>. Compact <binary stars> can lose orbital energy through <gravitational radiation> and merge, providing the <neutron star merger> route to heavy <r-process> material. Consequently chemical enrichment cannot be inferred entirely from isolated-star tracks, even when a simplified population calculation treats binary components as evolving independently.
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