(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
(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
Chemistry for Engineering Students
4th Edition
ISBN:9781337398909
Author:Lawrence S. Brown, Tom Holme
Publisher:Lawrence S. Brown, Tom Holme
Chapter6: The Periodic Table And Atomic Structure
Section: Chapter Questions
Problem 6.93PAE: 6.93 A mercury atom is initially in its lowest possible (or ground state) energy level. The atom...
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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 \( n = 3 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc0d9066b-5fdf-42a6-b05e-754bdfae176c%2F0265c92f-daa6-4522-9c3b-ea66a16022d8%2F8ee66z_processed.jpeg&w=3840&q=75)
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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