Final answer:
Electron-degenerate matter forms in the carbon core of a solar-mass red supergiant when the core contracts and the electrons resist further compression, supporting the core via electron degeneracy pressure until no further nuclear reactions occur, ultimately leaving behind a white dwarf.
Step-by-step explanation:
The formation of electron-degenerate matter in the carbon core of a solar-mass red supergiant occurs when nuclear reactions cease and the star's core contracts. The intense gravitational forces try to compress the core further, causing the electrons to be packed more closely. However, due to the Pauli exclusion principle, the electrons resist this compression, creating a degenerate gas where the resulting electron-degenerate pressure supports the core. This state predominates until no further fusion processes can occur, leaving behind a white dwarf, an incredibly dense object supported by electron degeneracy pressure.
For more massive stars, specifically those with initial masses over 10 Msun, the core is composed primarily of iron, formed from successive nuclear fusion reactions. In contrast, stars with masses ranging from 8 to 10 Msun likely have cores of oxygen, neon, and magnesium, as they do not reach the temperatures required to fuse elements as heavy as iron. However, once the iron core of an extremely massive star reaches a critical density, even electron degeneracy pressure cannot support it further. This leads to a core collapse, producing a neutron star or triggering a supernova explosion, depending on the mass of the star.