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 Content: Calculating Energy of Photons
#### Question:
What is the energy in kJ/mole of photons associated with red light of wavelength \(6.35 \times 10^2\) nm? *Show your work for full credit.*
#### Explanation:
To solve this problem, you need to follow these steps using the formulae related to photon energy:
1. **Convert Wavelength to Meters:**
The given wavelength is \(6.35 \times 10^2\) nm, which is \(6.35 \times 10^{-7}\) meters (as \(1 \, \text{nm} = 10^{-9} \, \text{m}\)).
2. **Use the Energy Formula:**
The energy of a photon can be calculated using the formula:
\[
E = \frac{hc}{\lambda}
\]
Where:
- \(E\) is the energy of the photon in Joules (J)
- \(h\) is Planck’s constant, \(6.626 \times 10^{-34}\) J·s
- \(c\) is the speed of light, \(3.00 \times 10^8\) m/s
- \(\lambda\) is the wavelength in meters
3. **Calculate Energy per Photon:**
Substitute the values into the formula to calculate the energy per photon.
4. **Convert to Energy per Mole:**
Since 1 mole of photons contains Avogadro's number (\(6.022 \times 10^{23}\) mol\(^{-1}\)), multiply the energy of one photon by Avogadro's number to obtain the energy in Joules per mole.
5. **Convert Joules to Kilojoules:**
Convert the energy from Joules to kilojoules by dividing by 1000.
Once you have calculated these steps, you will find the energy in kJ/mole for the red light photons given. Remember to present your work clearly for full credit.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F107b68ef-5916-46d8-b604-d8abbf265ef5%2F3a674b17-f796-4764-8507-0cd4d5300b91%2Fpb45ctd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Educational Content: Calculating Energy of Photons
#### Question:
What is the energy in kJ/mole of photons associated with red light of wavelength \(6.35 \times 10^2\) nm? *Show your work for full credit.*
#### Explanation:
To solve this problem, you need to follow these steps using the formulae related to photon energy:
1. **Convert Wavelength to Meters:**
The given wavelength is \(6.35 \times 10^2\) nm, which is \(6.35 \times 10^{-7}\) meters (as \(1 \, \text{nm} = 10^{-9} \, \text{m}\)).
2. **Use the Energy Formula:**
The energy of a photon can be calculated using the formula:
\[
E = \frac{hc}{\lambda}
\]
Where:
- \(E\) is the energy of the photon in Joules (J)
- \(h\) is Planck’s constant, \(6.626 \times 10^{-34}\) J·s
- \(c\) is the speed of light, \(3.00 \times 10^8\) m/s
- \(\lambda\) is the wavelength in meters
3. **Calculate Energy per Photon:**
Substitute the values into the formula to calculate the energy per photon.
4. **Convert to Energy per Mole:**
Since 1 mole of photons contains Avogadro's number (\(6.022 \times 10^{23}\) mol\(^{-1}\)), multiply the energy of one photon by Avogadro's number to obtain the energy in Joules per mole.
5. **Convert Joules to Kilojoules:**
Convert the energy from Joules to kilojoules by dividing by 1000.
Once you have calculated these steps, you will find the energy in kJ/mole for the red light photons given. Remember to present your work clearly for full credit.
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