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...
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![**Transcription for Educational Website:**
---
**Problem Statement**
- **Electron Transition in Hydrogen:**
- Initial Energy Level \( n = 8 \)
- Final Energy Level \( n = 4 \)
- **Constants:**
- \( R_H = 2.18 \times 10^{-18} \, \text{J} \) (Rydberg constant for hydrogen)
- Speed of light \( = 3.0 \times 10^8 \, \text{m/s} \)
**Task:**
Calculate the wavelength of the light emitted during this transition.
---
**Explanation for Calculation:**
To find the wavelength of light emitted when an electron transitions between two energy levels in a hydrogen atom, use the following formula derived from the Rydberg formula for hydrogen:
\[
\frac{1}{\lambda} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)
\]
Where:
- \( \lambda \) is the wavelength of light emitted,
- \( R_H \) is the Rydberg constant,
- \( n_1 \) and \( n_2 \) are the principal quantum numbers of the initial and final energy levels respectively.
**Application:**
Substitute the given values of \( n_1 = 4 \) and \( n_2 = 8 \) and solve for \( \lambda \).
Following this, use the relationship between frequency (\( f \)), speed of light (\( c \)), and wavelength (\( \lambda \)):
\[
\lambda = \frac{c}{f}
\]
Where:
- \( c = 3.0 \times 10^8 \, \text{m/s} \)
This calculation will provide the wavelength of the emitted light in meters.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff7e0b628-1887-4036-8cfa-486903c53c1e%2F645cd123-60f9-4740-a7b6-d154aee6c973%2Fy0a01l8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Transcription for Educational Website:**
---
**Problem Statement**
- **Electron Transition in Hydrogen:**
- Initial Energy Level \( n = 8 \)
- Final Energy Level \( n = 4 \)
- **Constants:**
- \( R_H = 2.18 \times 10^{-18} \, \text{J} \) (Rydberg constant for hydrogen)
- Speed of light \( = 3.0 \times 10^8 \, \text{m/s} \)
**Task:**
Calculate the wavelength of the light emitted during this transition.
---
**Explanation for Calculation:**
To find the wavelength of light emitted when an electron transitions between two energy levels in a hydrogen atom, use the following formula derived from the Rydberg formula for hydrogen:
\[
\frac{1}{\lambda} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)
\]
Where:
- \( \lambda \) is the wavelength of light emitted,
- \( R_H \) is the Rydberg constant,
- \( n_1 \) and \( n_2 \) are the principal quantum numbers of the initial and final energy levels respectively.
**Application:**
Substitute the given values of \( n_1 = 4 \) and \( n_2 = 8 \) and solve for \( \lambda \).
Following this, use the relationship between frequency (\( f \)), speed of light (\( c \)), and wavelength (\( \lambda \)):
\[
\lambda = \frac{c}{f}
\]
Where:
- \( c = 3.0 \times 10^8 \, \text{m/s} \)
This calculation will provide the wavelength of the emitted light in meters.
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