(8.3)Which of the following transitions (in a hydrogen atom) represent emission of the photon with the longest wavelength? E n = ∞ n = 5 n = 4 n=3 n = 2 n=1

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**Educational Content: Photon Emission in Hydrogen Atoms**

**Question (8.3):**
Which of the following transitions (in a hydrogen atom) represent emission of the photon with the longest wavelength?

**Explanation of Graph/Diagram:**
The diagram on the left depicts energy levels of electrons in a hydrogen atom. The vertical axis is labeled as \(E_n\) representing energy levels corresponding to different principal quantum numbers (n). The lines are labeled with different \( n \) values:

- \( n = \infty \)
- \( n = 5 \)
- \( n = 4 \)
- \( n = 3 \)
- \( n = 2 \)
- \( n = 1 \)

Transitions between these energy levels result in the emission or absorption of photons.

**Answer Choices:**
- \( \bigcirc \) \( n = 3 \) to \( n = 1 \)
- \( \bigcirc \) \( n = 4 \) to \( n = 3 \)
- \( \bigcirc \) \( n = 1 \) to \( n = 2 \)
- \( \bigcirc \) \( n = 5 \) to \( n = 2 \)

**Explanation:**

In atomic physics, the wavelength of the photon emitted during a transition between two energy levels in a hydrogen atom is inversely proportional to the difference in the energy levels. This is described by the equation:

\[ \frac{1}{\lambda} = R_H \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right) \]

Where:
- \( \lambda \) is the wavelength of the emitted photon.
- \( R_H \) is the Rydberg constant for hydrogen.
- \( n_f \) is the final energy level.
- \( n_i \) is the initial energy level.

The longest wavelength corresponds to the smallest energy difference.

**Thus, the transition that represents emission of the photon with the longest wavelength is:**

\[ \bigcirc \) \( n = 4 \) to \( n = 3 \)
Transcribed Image Text:**Educational Content: Photon Emission in Hydrogen Atoms** **Question (8.3):** Which of the following transitions (in a hydrogen atom) represent emission of the photon with the longest wavelength? **Explanation of Graph/Diagram:** The diagram on the left depicts energy levels of electrons in a hydrogen atom. The vertical axis is labeled as \(E_n\) representing energy levels corresponding to different principal quantum numbers (n). The lines are labeled with different \( n \) values: - \( n = \infty \) - \( n = 5 \) - \( n = 4 \) - \( n = 3 \) - \( n = 2 \) - \( n = 1 \) Transitions between these energy levels result in the emission or absorption of photons. **Answer Choices:** - \( \bigcirc \) \( n = 3 \) to \( n = 1 \) - \( \bigcirc \) \( n = 4 \) to \( n = 3 \) - \( \bigcirc \) \( n = 1 \) to \( n = 2 \) - \( \bigcirc \) \( n = 5 \) to \( n = 2 \) **Explanation:** In atomic physics, the wavelength of the photon emitted during a transition between two energy levels in a hydrogen atom is inversely proportional to the difference in the energy levels. This is described by the equation: \[ \frac{1}{\lambda} = R_H \left( \frac{1}{n_f^2} - \frac{1}{n_i^2} \right) \] Where: - \( \lambda \) is the wavelength of the emitted photon. - \( R_H \) is the Rydberg constant for hydrogen. - \( n_f \) is the final energy level. - \( n_i \) is the initial energy level. The longest wavelength corresponds to the smallest energy difference. **Thus, the transition that represents emission of the photon with the longest wavelength is:** \[ \bigcirc \) \( n = 4 \) to \( n = 3 \)
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