Consider the following statements:Statement I: Giant stars live much longer than dwarf stars.Stateme

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Question

Consider the following statements:Statement I: Giant stars live much longer than dwarf stars.Statement II: Compared to dwarf stars, giant stars have a greater rate of nuclear reactions.Which one of the following is correct in respect of the above statements?

Accepted Answer

Correct Answer: D — Statement I is incorrect but Statement II is correctStep-by-step Solution:Statement I — Giant stars live much longer than dwarf stars: This is incorrect. The relationship is actually the opposite. Giant stars (massive stars) have much shorter lifespans than dwarf stars (smaller, low-mass stars). The reason is counter-intuitive: although giant stars start with far more hydrogen fuel, they burn through it much faster due to their higher core temperatures and pressures. A massive star of 10 solar masses may live only 20–30 million years, while our Sun (a G-type dwarf) will live about 10 billion years, and a small red dwarf star (M-type) can live over 100 billion years. The stellar lifetime scales roughly as M^(–2.5) — the more massive, the shorter-lived. ✗Statement II — Giant stars have a greater rate of nuclear reactions than dwarf stars: This is correct. Massive giant stars have much hotter and denser cores than smaller dwarf stars. This drives faster proton-proton chain (pp-chain) and CNO cycle (carbon-nitrogen-oxygen cycle) nuclear fusion reactions — burning through hydrogen fuel at a much faster rate per unit mass. Giant stars also proceed to fuse helium, carbon, neon, oxygen, and silicon in successive shells — reactions not available to low-mass stars. The intense rate of nuclear burning is precisely what makes giant stars so luminous but so short-lived. ✓Why other options are incorrect:Option A: Incorrect. Statement I is wrong — giant stars live shorter, not longer than dwarf stars.Option B: Incorrect. Statement I is incorrect.Option C: Incorrect. Statement II is correct — giant stars do have greater rates of nuclear reactions.Key Concept: Stellar evolution and lifetimes: Star lifetime ∝ (Mass / Luminosity) ∝ M^(–2.5) approximately; Higher mass → shorter life. Star types by mass (solar masses, M☉): Red dwarf (0.08–0.8 M☉): Lifetime > 100 billion years; Sun-like (G-type, ~1 M☉): ~10 billion years; Intermediate (2–8 M☉): ~1 billion years; Massive stars (8–100+ M☉): Millions of years. End states: Low-mass stars ( 8 M☉): Red supergiant → supernova → neutron star or black hole. Nuclear fusion in stars: Low-mass stars: Proton-proton (pp) chain (hydrogen → helium); High-mass stars: pp-chain + CNO cycle (faster); Later stages: Helium fusion (triple-alpha process), carbon burning, oxygen burning, silicon burning → iron core (no more energy release → supernova). Hertzsprung-Russell (H-R) diagram: Main sequence — where stars spend most of their lives fusing hydrogen; Giants/supergiants are off the main sequence to the upper right; White dwarfs are below-left.

Consider the following statements:Statement I: Giant stars live much longer than dwarf stars.Statement II: Compared to dwarf stars, giant stars have a greater rate of nuclear reactions.Which one of the following is correct in respect of the above statements?

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Consider the following statements:Statement I: Giant stars live much longer than dwarf stars.Statement II: Compared to dwarf stars, giant stars have a greater rate of nuclear reactions.Which one of the following is correct in respect of the above statements?

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