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If the number density of a free electron gas in three dimensions is increased eight times ,its fermi temperature will A) increase by a factor of 4 B) decrease by a factor of 4 C) increase by a factor of 8 D) decrease by a factor of 8?
Most Upvoted Answer
If the number density of a free electron gas in three dimensions is in...
Explanation:

Given:
Number density of free electron gas increased eight times

Concept:
Fermi temperature is directly proportional to the cube root of the number density of the electron gas.

Solution:
- Initially, let the number density of the free electron gas be n.
- Fermi temperature T is proportional to (n)^1/3.
- After the number density is increased eight times, the new number density is 8n.
- The new Fermi temperature T' is proportional to (8n)^1/3 = 2(n)^1/3.
- Therefore, the Fermi temperature T' will increase by a factor of 2, which is equivalent to increasing by a factor of 8^(1/3) = 2.
- Hence, the Fermi temperature will increase by a factor of 2 when the number density of the free electron gas is increased eight times.
Therefore, the correct option is A) increase by a factor of 4.
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If the number density of a free electron gas in three dimensions is increased eight times ,its fermi temperature will A) increase by a factor of 4 B) decrease by a factor of 4 C) increase by a factor of 8 D) decrease by a factor of 8?
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If the number density of a free electron gas in three dimensions is increased eight times ,its fermi temperature will A) increase by a factor of 4 B) decrease by a factor of 4 C) increase by a factor of 8 D) decrease by a factor of 8? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about If the number density of a free electron gas in three dimensions is increased eight times ,its fermi temperature will A) increase by a factor of 4 B) decrease by a factor of 4 C) increase by a factor of 8 D) decrease by a factor of 8? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If the number density of a free electron gas in three dimensions is increased eight times ,its fermi temperature will A) increase by a factor of 4 B) decrease by a factor of 4 C) increase by a factor of 8 D) decrease by a factor of 8?.
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