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?

(a) Both Statement-I and Statement-II are correct and Statement-II explains Statement-I
(b) Both Statement-I and Statement-II are correct, but Statement-II does not explain Statement-I
(c) Statement-I is correct, but Statement-II is incorrect
(d) Statement-I is incorrect, but Statement-II is correct

Correct Answer: (d) Statement-I is incorrect, but Statement-II is correct

Explanation:

Statement-I: Giant stars live much longer than dwarf stars.
- This statement is incorrect. Giant stars have shorter lifespans compared to dwarf stars. Giant stars, due to their massive size and higher core temperatures, burn through their nuclear fuel much faster, resulting in shorter lifetimes. For example, a star with 10 times the mass of the Sun may only live for about 20 million years, whereas a red dwarf, which is much smaller, can last for 80 to 100 billion years, far exceeding the current age of the universe .
Statement-II: Compared to dwarf stars, giant stars have a greater rate of nuclear reactions.
- This statement is correct. Giant stars have hotter and denser cores, leading to a greater rate of nuclear reactions. This increased rate of nuclear fusion causes them to burn through their fuel more quickly than dwarf stars. For instance, a giant star can be thousands of times more luminous than the Sun due to its rapid nuclear reactions .

Analysis of Options:

(a) Both Statement-I and Statement-II are correct and Statement-II explains Statement-I
- This option is incorrect because Statement-I is incorrect.
(b) Both Statement-I and Statement-II are correct, but Statement-II does not explain Statement-I
- This option is incorrect because Statement-I is incorrect.
(c) Statement-I is correct, but Statement-II is incorrect
- This option is incorrect because Statement-I is incorrect and Statement-II is correct.
(d) Statement-I is incorrect, but Statement-II is correct
- This option is correct because Statement-I is incorrect and Statement-II is correct.

Learn more

Lifespan of Stars:
- Massive stars have shorter lifespans due to their rapid consumption of nuclear fuel. For example, stars with masses 10 times that of the Sun may only live for a few million years .
- Dwarf stars, especially red dwarfs, have longer lifespans. They burn their fuel slowly and can last for tens to hundreds of billions of years, far exceeding the current age of the universe .
Nuclear Reactions in Stars:
- Giant stars have higher core temperatures and greater rates of nuclear reactions. This results in higher luminosity and faster fuel consumption .
- Dwarf stars have lower core temperatures and slower rates of nuclear reactions, leading to longer lifespans .
Types of Stars:
- Giant stars include red giants, blue giants, and supergiants. They are characterized by their large radii and high luminosities .
- Dwarf stars include red dwarfs, yellow dwarfs (like the Sun), and white dwarfs. They are smaller and less luminous compared to giant stars.
Stellar Evolution:
- Massive stars end their lives in supernova explosions, leaving behind neutron stars or black holes .
- Smaller stars like the Sun will become red giants and eventually shed their outer layers, leaving behind a white dwarf .