When the hydrogen in a star's core is used up, the star goes through a series of changes depending on its mass. However, one of the most common outcomes is that the core of the star will contract and heat up, causing the outer layers of the star to expand and cool down. This results in the star becoming a red giant.
Specifically, as the hydrogen in the core is used up, the core contracts and heats up. This causes the outer layers of the star to expand and cool, increasing the star's radius and decreasing its surface temperature. This is known as the red giant phase.
Therefore, the correct answer is C. The helium core collapses and the outer layer expands into a red giant. Note that in more massive stars, the core may continue to contract and heat up until it reaches a critical point, leading to a supernova explosion. And in lower-mass stars, the outer layers may simply drift away, leaving behind a hot, dense white dwarf core.