(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
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
icon
Related questions
icon
Concept explainers
Question
**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 \( n = 3 \)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

Blurred answer
Knowledge Booster
Introduction and Principles of Quantum Theory
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Chemistry
Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Chemistry
Chemistry
Chemistry
ISBN:
9781259911156
Author:
Raymond Chang Dr., Jason Overby Professor
Publisher:
McGraw-Hill Education
Principles of Instrumental Analysis
Principles of Instrumental Analysis
Chemistry
ISBN:
9781305577213
Author:
Douglas A. Skoog, F. James Holler, Stanley R. Crouch
Publisher:
Cengage Learning
Organic Chemistry
Organic Chemistry
Chemistry
ISBN:
9780078021558
Author:
Janice Gorzynski Smith Dr.
Publisher:
McGraw-Hill Education
Chemistry: Principles and Reactions
Chemistry: Principles and Reactions
Chemistry
ISBN:
9781305079373
Author:
William L. Masterton, Cecile N. Hurley
Publisher:
Cengage Learning
Elementary Principles of Chemical Processes, Bind…
Elementary Principles of Chemical Processes, Bind…
Chemistry
ISBN:
9781118431221
Author:
Richard M. Felder, Ronald W. Rousseau, Lisa G. Bullard
Publisher:
WILEY