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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![**Educational Website Content**
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**Physics Problem: Calculating Photon Energy**
**Assignment Score:** 11.4%
**Question 10 of 35**
**Problem Statement:**
Calculate the energy of a photon emitted when an electron in a hydrogen atom undergoes a transition from \( n = 5 \) to \( n = 1 \).
**Energy Calculation:**
\( \text{Energy emitted:} \) [Enter your answer in the box provided] \( J \)
---
**How to Approach:**
To solve this problem, use the formula for the energy difference between two electron energy levels in a hydrogen atom:
\[
E = -13.6 \times \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right) \quad \text{eV}
\]
Where:
- \( n_1 = 1 \) is the final energy level.
- \( n_2 = 5 \) is the initial energy level.
- \( 13.6 \, \text{eV} \) is the ionization energy of hydrogen.
Convert your final answer from electronvolts to joules using the conversion:
1 eV = \( 1.602 \times 10^{-19} \) J.
**Note:**
This question tests your understanding of quantum transitions in hydrogen atoms, an essential topic in quantum mechanics.
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Transcribed Image Text:**Educational Website Content**
---
**Physics Problem: Calculating Photon Energy**
**Assignment Score:** 11.4%
**Question 10 of 35**
**Problem Statement:**
Calculate the energy of a photon emitted when an electron in a hydrogen atom undergoes a transition from \( n = 5 \) to \( n = 1 \).
**Energy Calculation:**
\( \text{Energy emitted:} \) [Enter your answer in the box provided] \( J \)
---
**How to Approach:**
To solve this problem, use the formula for the energy difference between two electron energy levels in a hydrogen atom:
\[
E = -13.6 \times \left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right) \quad \text{eV}
\]
Where:
- \( n_1 = 1 \) is the final energy level.
- \( n_2 = 5 \) is the initial energy level.
- \( 13.6 \, \text{eV} \) is the ionization energy of hydrogen.
Convert your final answer from electronvolts to joules using the conversion:
1 eV = \( 1.602 \times 10^{-19} \) J.
**Note:**
This question tests your understanding of quantum transitions in hydrogen atoms, an essential topic in quantum mechanics.
---
Expert Solution
Step 1
Using the Rydberg's equation we get the energy
Step by step
Solved in 2 steps with 1 images
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