Unit 2: Stars and Stellar Evolution

Answer: A — The correct answer is A) Red Giant because when a star exhausts its hydrogen fuel, it expands to become a red giant, fusing helium into heavier elements. The other options are incorrect because a white dwarf is the remnants of a star after it has shed its outer layers, a neutron star is formed from the core of a massive star after a supernova explosion, and a black hole is a region of spacetime with such strong gravity that not even light can escape, not a stage in the life cycle of a typical star.

Answer: D — The correct answer applies the Stefan-Boltzmann law: L = 4πR²σT⁴. Equal luminosity with different temperatures requires inverse relationships between surface area and temperature. Star A (blue/hot) must be smaller, while Star B (red/cool) must be larger for their luminosities to be equal. Option A confuses apparent brightness with luminosity (an intrinsic property). Option B incorrectly states the relationship—a smaller star with higher temperature would have greater luminosity than a larger cooler star. Option C misidentifies Star B as a white dwarf when white dwarfs are actually small and hot; this conflates stellar classification with luminosity relationships. Only option D correctly demonstrates understanding that luminosity depends on both surface area and temperature, allowing different stellar configurations to produce identical luminous outputs.

Answer: B — The correct answer is B. The question establishes that both stars have identical luminosity (intrinsic brightness), yet Star A appears brighter. This directly tests understanding of the distinction between luminosity and apparent brightness. The inverse square law governs how brightness appears to decrease with distance (brightness ∝ 1/distance²), so Star A's greater apparent brightness must result from it being closer to Earth. Why the others are incorrect: A) Confuses mass with luminosity and ignores that the stars were stated to have equal luminosity; B) Correctly applies the inverse square law and distinguishes intrinsic from apparent brightness; C) Misunderstands that identical luminosity doesn't indicate identical temperature—temperature affects luminosity but isn't the only determining factor, and temperature wouldn't explain differing apparent brightnesses if luminosity is equal; D) Incorrectly assumes surface area is the primary determinant of apparent brightness and ignores distance effects. This question tests the critical ability to distinguish between luminosity (intrinsic) and apparent brightness (distance-dependent), a foundational concept in stellar astronomy.

Answer: B — The correct answer is B because once a star like our Sun exhausts its hydrogen fuel, it expands into a red giant and then sheds its outer layers, leaving behind a core known as a white dwarf. This is the expected evolutionary path for low-mass stars like our Sun. Option A is incorrect because a star would need to be much more massive to form a black hole. Option C is incorrect because while some stars do end their lives as supernovae and leave behind neutron stars, this typically occurs for more massive stars. Option D is incorrect because a star cannot contract back into a main-sequence star once it has exhausted its hydrogen fuel and expanded into a red giant.

Answer: B — Correct Answer (B): The Stefan-Boltzmann law shows that luminosity depends on both radius and temperature (L ∝ R²T⁴). Since Star A has the same luminosity as Star B but much lower temperature, it must compensate with a significantly larger radius. Specifically, Star A would need to be roughly 9 times larger in radius than Star B (since the T⁴ term differs by a factor of ~81, requiring an R² compensation of ~81). This is consistent with Star A being a giant or supergiant while Star B is a main-sequence star or dwarf. Why the other options are incorrect: Option A misunderstands stellar density and classification. White dwarfs are extremely hot (not cool at 3,000 K) and have small radii despite high temperature. A 3,000 K star is actually a cool red giant, not a dense white dwarf. Option C contradicts the observation stated in the problem. Both stars have identical luminosities by definition. Temperature is not the only factor—radius also plays a crucial role in the Stefan-Boltzmann relationship. Option D assumes evolutionary stage correlates only with luminosity, ignoring that the H-R diagram uses both luminosity AND temperature to classify stars. Two stars with the same luminosity but different temperatures occupy different positions on the H-R diagram and represent different evolutionary stages or stellar types.