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...
Related questions
Question
![**Title: Understanding Photon Energy and Wavelengths**
Some chemical reactions, such as the formation of ozone in Earth's stratosphere, can be initiated by light that has a wavelength less than a specific value. To comprehend how this process works, it's essential to calculate the longest wavelength (in nanometers) that can provide an energy of at least 420 kJ/mol.
### Problem Statement
Calculate the longest wavelength (nm) that can provide an energy of at least 420 kJ/mol.
---
### Calculation Steps
1. **Question:** What is the frequency of light, in hertz, that has the necessary energy?
Given:
\[
E = 6.098 \times 10^{-19} \, \text{J/photon}
\]
2. **Correction Needed:**
- The initial frequency calculation was incorrect.
3. **Hint:** Use Planck's equation:
\[
E = h \nu = \frac{E}{h}
\]
To determine the frequency.
4. **Constants:**
- Planck's constant, \( h = 6.626 \times 10^{-34} \, \text{J}\cdot\text{s} \)
**Approach:**
- Use the energy value and Planck's constant to find the frequency.
- Convert the energy per mole to energy per photon if necessary.
- Calculate the corresponding wavelength using the speed of light if needed.
This example demonstrates the importance of accurately calculating the frequency or wavelength necessary for initiating specific chemical reactions with light energy.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F29cd9eeb-c72b-48cd-b80d-b19cf468f6ca%2F6cb9d584-279e-41cc-9bfe-3ce99ff4aaff%2Frt0kpc.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Understanding Photon Energy and Wavelengths**
Some chemical reactions, such as the formation of ozone in Earth's stratosphere, can be initiated by light that has a wavelength less than a specific value. To comprehend how this process works, it's essential to calculate the longest wavelength (in nanometers) that can provide an energy of at least 420 kJ/mol.
### Problem Statement
Calculate the longest wavelength (nm) that can provide an energy of at least 420 kJ/mol.
---
### Calculation Steps
1. **Question:** What is the frequency of light, in hertz, that has the necessary energy?
Given:
\[
E = 6.098 \times 10^{-19} \, \text{J/photon}
\]
2. **Correction Needed:**
- The initial frequency calculation was incorrect.
3. **Hint:** Use Planck's equation:
\[
E = h \nu = \frac{E}{h}
\]
To determine the frequency.
4. **Constants:**
- Planck's constant, \( h = 6.626 \times 10^{-34} \, \text{J}\cdot\text{s} \)
**Approach:**
- Use the energy value and Planck's constant to find the frequency.
- Convert the energy per mole to energy per photon if necessary.
- Calculate the corresponding wavelength using the speed of light if needed.
This example demonstrates the importance of accurately calculating the frequency or wavelength necessary for initiating specific chemical reactions with light energy.
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