mPEC Forum

ฟิสิกส์โอลิมปิก วิทยาศาสตร์โอลิมปิก ข้อสอบแข่งขัน ข้อสอบชิงทุน => GRE - Physics => Topic started by: conantee on January 04, 2010, 04:29:18 AM

Title: GR8677.055
Post by: conantee on January 04, 2010, 04:29:18 AM
55. The mean kinetic energy of electrons in metals at room temperature is usually many times the thermal energy kT. Which of the following can best be used to explain this fact?
(A) The energy-time uncertainty relation
(B) The Pauli exclusion principle
(C) The degeneracy of the energy levels
(D) The Born approximation
(E) The wave-particle duality

Title: Re: GR8677.055
Post by: conantee on February 01, 2010, 08:05:39 AM
This question requires more knowledge about solid state physics, but you can eliminate some choices if you know some definitions of words appeared in choices
First, Born approximation is used in scattering theory - not related to subject we are talking about. So, (E) is wrong.
Second, degeneracy of energy levels implies that many states has same energy. This makes the mean energy of systems decreases compared to non-degenerated one. So, (C) is wrong.
Third, energy-time uncertainty relation may infer the energy of electron via its uncertainty. However, there is no time uncertainty mentioned in the problem. So, (A) is wrong.
(E) sounds too general.

The right answer is (B). Since electrons cannot be in the same states. Free electrons in metal needs to occupy other state and piles up to state with higher and higher energy. That is why mean energy becomes large compare to thermal energy.

The correct answer is (B). 30 of 100 got the correct one.