Nicely done, coderancher. Going supernova or becoming a black hole is typical of stars with 10 or more times the mass of our Sun.
A nova is an event that may happen when white dwarfs are part of a binary system and pull hydrogen from their partner.
As you said, our Sun is not massive enough to fuse carbon. Furthermore (to clarify something from a previous poster), it is not old enough to be fusing helium to any appreciable degree. Helium fusion will occur later when the Sun's supply of hydrogen fuel is diminished to the point that gravity overwhelms thermal pressure and the Sun begins to collapse. As it collapses, the temperature of the core will eventually become high enough to support the fusion of helium into carbon. This will cause a huge increase in temperature, causing the Sun to expand again into a red giant.
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