L14 Exchange and Coulomb Interactions Quiz
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Questions and Answers

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?

  • 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?

  • 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?

    <p>Bosons</p> Signup and view all the answers

    How does exchanging labels of a pair of electrons affect the wavefunction?

    <p>It has no effect on the wavefunction.</p> Signup and view all the answers

    What is the reason for the wavefunction of a multielectron atom to be anti-symmetric with respect to particle exchange?

    <p>To satisfy the Pauli exclusion principle for fermions</p> Signup and view all the answers

    In the ground state of helium, what is the configuration of the two electrons?

    <p>1s2</p> Signup and view all the answers

    What is the total wavefunction for an excited helium atom with one electron in the higher shell?

    <p>$\Psi = \frac{1}{\sqrt{2}}(\psi_{\alpha}(r_1)\psi_{\beta}(r_2) + \psi_{\beta}(r_1)\psi_{\alpha}(r_2))$</p> Signup and view all the answers

    What does it mean when the total wavefunction for a two-electron system is anti-symmetrical?

    <p>The spin of one electron is up and the other is down</p> Signup and view all the answers

    What is the value of the total spin ($S$) for a two-electron system if $S = 0$?

    <p>$S = 0$</p> Signup and view all the answers

    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.

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    Description

    Test your knowledge about exchange and Coulomb interactions, which are types of interatomic interactions that occur between atoms or ions. This quiz covers the interaction between charged particles due to their electric fields, as well as the exchange interaction related to the Pauli exclusion principle.

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