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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- ABoth Statement-I and Statement-II are correct and Statement-I Statement-II explains
- BBoth Statement-I and Statement-II are correct, but Statement-II does not explain Statement-I
- CStatement-I is correct, but Statement-II is incorrect
- DStatement-I is incorrect, but Statement-II is correct
Show answer
Answer: (D) Statement-I is incorrect, but Statement-II is correct
Correct Answer: (d) Statement-I is incorrect, Statement-II is correct.
Statement I:
Giant stars live much longer than dwarf stars — ✗ WRONG.
It's the opposite.
Giant stars burn through their fuel much faster because of their enormous energy output, so they have shorter lifespans (millions of years).
Dwarf stars like our Sun live for billions of years.
Statement II:
Giant stars have a greater rate of nuclear reactions — ✓ CORRECT.
Their cores are hotter and denser, driving faster fusion reactions.
The logic:
- More mass
- hotter core
- faster fuel burning
- shorter life.
Think of it like a candle — a bigger flame burns through wax faster.
Giant stars burn fuel faster due to higher core temperatures and pressures, giving them lifespans of only millions of years compared to billions for dwarf stars.
The question tests the counterintuitive relationship between stellar mass and lifespan - bigger stars die younger despite having more fuel.
Giant Stars vs Dwarf Stars
Science And Technology Giant stars dwarf stars
Giant Stars vs Dwarf Stars: Classification & Key Differences
Giant stars are massive, bright, and have short lifespans (millions of years)
Dwarf stars are smaller, dimmer, and have long lifespans (billions of years)
Mass determines lifespan: More mass = faster fuel consumption = shorter life
Our Sun is a dwarf star (yellow dwarf) with ~10 billion year lifespan
Basic Classification
Stars are classified by size, mass, and brightness. The key distinction is that stellar mass determines both energy output and lifespan in an inverse relationship.
Giant vs Dwarf Comparison
Feature | Giant Stars | Dwarf Stars |
|---|---|---|
Mass | 8+ times Sun's mass | 0.1 to 8 times Sun's mass |
Size | 10-100 times Sun's radius | Similar or smaller than Sun |
Brightness | Extremely bright | Moderate to dim |
Core Temperature | Very high (faster reactions) | Lower (slower reactions) |
Lifespan | Millions of years | Billions of years |
Examples | Rigel, Betelgeuse | Sun, Proxima Centauri |
Trap: Assuming bigger stars live longer - it's the opposite
Trap: Confusing brightness with lifespan - brighter stars burn out faster
Statement-II explains Statement-I trap - faster reactions cause shorter life, not longer
Nuclear Fusion in Stellar Cores
Science And Technology nuclear reactions rate of nuclear reactions
Nuclear Fusion in Stars: How Mass Affects Reaction Rates
Nuclear fusion converts hydrogen to helium in stellar cores
Higher mass = hotter core = faster fusion reactions
Giant stars have much faster reaction rates than dwarf stars
Fusion Mechanism
Stars generate energy by nuclear fusion - converting hydrogen nuclei into helium in their cores. The reaction rate depends critically on core temperature and pressure, both determined by stellar mass.
Mass-to-Energy Chain
%%{init: {"flowchart": {"wrappingWidth": 460}}}%%
flowchart TD
s1["`**Higher Stellar Mass**
More gravitational compression`"]
s2["`**Hotter, Denser Core**
Temperature reaches 15+ million Kelvin`"]
s3["`**Faster Nuclear Reactions**
Hydrogen fuses to helium rapidly`"]
s4["`**Greater Energy Output**
Higher luminosity and brightness`"]
s5["`**Faster Fuel Depletion**
Shorter stellar lifespan`"]
s1 --> s2
s2 --> s3
s3 --> s4
s4 --> s5Reaction Rate Factors
Temperature sensitivity: Fusion rate increases exponentially with core temperature
Pressure effects: Higher mass creates more gravitational pressure in core
Fuel consumption: Giant stars burn hydrogen millions of times faster than dwarf stars
Stellar Evolution & Lifecycles
Science And Technology
Stellar Evolution: From Birth to Death Based on Mass
Low-mass stars (like Sun) evolve slowly over billions of years
High-mass stars evolve rapidly and end in spectacular supernovas
Main sequence is the longest phase where stars burn hydrogen steadily
Evolution Overview
Stellar evolution is entirely determined by initial mass. This creates two distinct evolutionary pathways with dramatically different timescales and endpoints.
Evolution by Mass Category
Mass Category | Main Sequence Duration | Final Stage | End Process |
|---|---|---|---|
Low Mass (0.1-0.8 Solar masses) | Trillions of years | Red dwarf → White dwarf | Gradual cooling |
Sun-like (0.8-8 Solar masses) | Billions of years | Red giant → White dwarf | Planetary nebula |
High Mass (8-25 Solar masses) | Millions of years | Red supergiant → Neutron star | Supernova explosion |
Very High Mass (25+ Solar masses) | Few million years | Hypergiant → Black hole | Hypernova explosion |
Stellar Evolution
Source: | The Schools' Observatory — Stellar Evolution | The Schools' Observatory · www.schoolsobservatory.org
Statement Analysis in Science Questions
Science And Technology Statement-I Statement-II
Analyzing Scientific Statement Pairs: Logic & Causation
Check each statement independently for factual accuracy first
Then check if Statement-II logically explains Statement-I
Inverse relationships are common traps (more X causes less Y)
Analysis Method
UPSC tests both factual knowledge and logical reasoning. The key is distinguishing between correlation and causation, especially with inverse relationships.
Statement Analysis Steps
%%{init: {"flowchart": {"wrappingWidth": 460}}}%%
flowchart TD
s1["`**Evaluate Statement-I**
Is this factually correct? Check against known science`"]
s2["`**Evaluate Statement-II**
Is this factually correct? Independent of Statement-I`"]
s3["`**Check Logical Link**
Does Statement-II explain WHY Statement-I occurs?`"]
s4["`**Watch for Inversions**
Does Statement-II actually contradict Statement-I?`"]
s1 --> s2
s2 --> s3
s3 --> s4This Question's Logic
Statement-I was wrong: Giant stars actually live shorter lives than dwarf stars
Statement-II was correct: Giant stars do have faster nuclear reactions
No explanation link: Faster reactions cause shorter life, contradicting Statement-I
Inverse causation: When cause X increases effect Y decreases (mass vs lifespan)
True statements, wrong link: Both statements correct but unrelated or contradictory
Intuitive assumptions: Bigger/more doesn't always mean longer/better