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

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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?

It affects the alignment of the spins. 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?

$∆ 𝐸𝑒𝑥𝑐ℎ𝑎𝑛𝑔𝑒 = −2J_{\alpha \beta} S_{1ҧ} S_{2ҧ}$ 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?

$\Delta E = -\mu \cdot B$ Signup and view all the answers

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

$E_B v = v_0 \pm 4 \pi e B v_0$ 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?

Anomalous Zeeman effect Signup and view all the answers

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

The splitting of spectral lines in the presence of a magnetic field 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?

Normal Zeeman effect Signup and view all the answers

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?

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

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

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

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

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

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

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

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

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

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