The exclusion principle states that:
A) if the position of a particle is well known, its momentum will not be well known.
B) two photons cannot have the same quantum state at the same time.
C) only electrons in the same quantum state can be in the same place at the same time.
D) two neutrons cannot occupy the same quantum state at the same time.
The exclusion principle, also known as Pauli's exclusion principle, is a fundamental concept in quantum mechanics that applies to particles with half-integer spin, such as electrons, protons, and neutrons. It states that no two identical fermions (particles that obey the Pauli exclusion principle) can occupy the same quantum state simultaneously.
Let's go through each option to determine which one correctly describes the exclusion principle:
A) "If the position of a particle is well known, its momentum will not be well known." This statement is not related to the exclusion principle. It is known as the Heisenberg uncertainty principle, which states that there is a fundamental limit to the precision with which certain pairs of physical properties of a particle can be known simultaneously. This option is incorrect.
B) "Two photons cannot have the same quantum state at the same time." This statement is also incorrect. Photons are bosons, which follow different rules from fermions. Multiple photons can occupy the same quantum state at the same time, unlike fermions. Therefore, this option does not describe the exclusion principle.
C) "Only electrons in the same quantum state can be in the same place at the same time." This statement correctly captures the essence of the exclusion principle. Electrons, being fermions, obey Pauli's exclusion principle, which prevents two identical electrons from occupying the same quantum state simultaneously. Therefore, this option accurately describes the exclusion principle and is the correct answer.
D) "Two neutrons cannot occupy the same quantum state at the same time." This statement is similar to option C but with a substitution of electrons for neutrons. Like electrons, neutrons are also fermions and follow the exclusion principle. Thus, two neutrons cannot occupy the same quantum state at the same time. However, the question specifically mentions the exclusion principle, which is associated with electrons more directly. Therefore, this option is not the best description of the exclusion principle.
To summarize, the correct statement that describes the exclusion principle is option C: "Only electrons in the same quantum state can be in the same place at the same time."