Podcast
Questions and Answers
Which of the following best describes the exchange interaction?
Which of the following best describes the exchange interaction?
- It is a result of the Pauli inclusion principle for fermions.
- It arises from the indistinguishability of identical particles, such as electrons. (correct)
- It is related to the gravitational force between charged particles.
- It occurs when two different particles exchange their electric fields.
In the context of exchange interaction, what happens when two electrons have opposite spins?
In the context of exchange interaction, what happens when two electrons have opposite spins?
- The exchange interaction is attractive, leading to a lower total energy for the system. (correct)
- The exchange interaction has no effect on the total energy of the system.
- The exchange interaction depends on the distance between the electrons.
- The exchange interaction becomes repulsive due to the spin opposition.
How does the wave function of multi-electron atoms with exchange symmetry behave?
How does the wave function of multi-electron atoms with exchange symmetry behave?
- It exponentially decreases as the number of electrons increases.
- It must be antisymmetric with respect to particle exchange.
- It becomes symmetric with respect to particle exchange. (correct)
- It remains unaffected by the exchange symmetry of the electrons.
What type of particles have a positive wave function and are symmetric with respect to particle exchange?
What type of particles have a positive wave function and are symmetric with respect to particle exchange?
How does exchanging labels of a pair of electrons affect the wavefunction?
How does exchanging labels of a pair of electrons affect the wavefunction?
What is the reason for the wavefunction of a multielectron atom to be anti-symmetric with respect to particle exchange?
What is the reason for the wavefunction of a multielectron atom to be anti-symmetric with respect to particle exchange?
In the ground state of helium, what is the configuration of the two electrons?
In the ground state of helium, what is the configuration of the two electrons?
What is the total wavefunction for an excited helium atom with one electron in the higher shell?
What is the total wavefunction for an excited helium atom with one electron in the higher shell?
What does it mean when the total wavefunction for a two-electron system is anti-symmetrical?
What does it mean when the total wavefunction for a two-electron system is anti-symmetrical?
What is the value of the total spin ($S$) for a two-electron system if $S = 0$?
What is the value of the total spin ($S$) for a two-electron system if $S = 0$?
Flashcards are hidden until you start studying
Study Notes
Exchange Interaction
- Exchange interaction occurs when two electrons have opposite spins, resulting in a decrease in energy.
- When two electrons have opposite spins, the Coulomb repulsion between them is reduced, leading to an attraction between the electrons.
Wave Function of Multi-Electron Atoms
- The wave function of multi-electron atoms with exchange symmetry behaves according to the Pauli Exclusion Principle.
- The wave function of a multi-electron atom is anti-symmetric with respect to particle exchange.
Particle Exchange
- Bosons are particles that have a positive wave function and are symmetric with respect to particle exchange.
- Exchanging labels of a pair of electrons affects the wavefunction, making it anti-symmetric.
Multi-Electron Atoms
- The reason for the wavefunction of a multielectron atom to be anti-symmetric with respect to particle exchange is to satisfy the Pauli Exclusion Principle.
- In the ground state of helium, the two electrons have opposite spins and occupy the same orbital.
Excited Helium Atom
- The total wavefunction for an excited helium atom with one electron in the higher shell is a linear combination of the wavefunctions of the individual electrons.
Anti-Symmetrical Wavefunction
- When the total wavefunction for a two-electron system is anti-symmetrical, it means that exchanging the labels of the electrons changes the sign of the wavefunction.
- The value of the total spin (S) for a two-electron system is 0 when S = 0, indicating that the electrons have opposite spins.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
