SIF3002 Session 2023/24 L15: Exchange Energy and Spin States
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Questions and Answers

What is the total energy expression for the singlet state?

  • $-4E_R(\frac{1}{n_1^2} + \frac{1}{n_2^2} + D_{\alpha \beta} - J_{\alpha \beta})$
  • $-4E_R(\frac{1}{n_1^2} + \frac{1}{n_2^2} - D_{\alpha \beta} + J_{\alpha \beta})$
  • $-4E_R(\frac{1}{n_1^2} + \frac{1}{n_2^2} + D_{\alpha \beta} + J_{\alpha \beta})$ (correct)
  • $-4E_R(\frac{1}{n_1^2} + \frac{1}{n_2^2} - D_{\alpha \beta} - J_{\alpha \beta})$

What is the difference in energies for the singlet and triplet states?

  • $2J_{\alpha \beta}$ (correct)
  • $J_{\alpha \beta}$
  • $-J_{\alpha \beta}$
  • $-2J_{\alpha \beta}$

What is the measured value of the ground state energy for helium?

  • 76.98 eV
  • 77.98 eV
  • 78.98 eV (correct)
  • 75.98 eV

Why is exchange splitting a significant effect in the structure of the helium atom?

<p>It affects the alignment of the spins. (B)</p> Signup and view all the answers

How is exchange energy sometimes written to show the change of energy related to the alignment of the spins?

<p>$∆ 𝐸𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒 = −2J_{\alpha \beta} S_{1ҧ} S_{2ҧ}$ (B)</p> Signup and view all the answers

In the context of the Zeeman effect, what is the interaction energy between the magnetic moment and a uniform magnetic field?

<p>$\Delta E = -\mu \cdot B$ (A)</p> Signup and view all the answers

What is the formula for predicting the frequencies of the split component lines due to the Zeeman effect?

<p>$E_B v = v_0 \pm 4 \pi e B v_0$ (D)</p> Signup and view all the answers

What type of interaction between atoms and a magnetic field can be classified as depending on quantum mechanical effects?

<p>Anomalous Zeeman effect (A)</p> Signup and view all the answers

What does the Zeeman effect describe in the context of atomic physics?

<p>The splitting of spectral lines in the presence of a magnetic field (A)</p> Signup and view all the answers

What does the net spin of the active electron of an atom being equal to zero represent in the context of atomic physics?

<p>Normal Zeeman effect (D)</p> Signup and view all the answers

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