Welcome to Westonci.ca, your ultimate destination for finding answers to a wide range of questions from experts. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.
Sagot :
To determine the wavelength of a photon with an energy of [tex]\( 3.38 \times 10^{-19} \)[/tex] joules, we can use the relationship between energy [tex]\(E\)[/tex], Planck's constant [tex]\(h\)[/tex], and the speed of light [tex]\(c\)[/tex]. The formula to find the wavelength [tex]\(\lambda\)[/tex] of a photon is given by:
[tex]\[ \lambda = \frac{h \cdot c}{E} \][/tex]
where:
- [tex]\(E\)[/tex] is the energy of the photon,
- [tex]\(h\)[/tex] is Planck's constant ([tex]\(6.626 \times 10^{-34}\)[/tex] joule seconds),
- [tex]\(c\)[/tex] is the speed of light ([tex]\(3.00 \times 10^8\)[/tex] meters per second).
Step-by-Step Solution:
1. Identify the given values:
- Energy [tex]\(E = 3.38 \times 10^{-19}\)[/tex] joules
- Planck's constant [tex]\(h = 6.626 \times 10^{-34}\)[/tex] joule seconds
- Speed of light [tex]\(c = 3.00 \times 10^8\)[/tex] meters per second
2. Plug the values into the wavelength formula:
[tex]\[ \lambda = \frac{6.626 \times 10^{-34} \, \text{Js} \times 3.00 \times 10^8 \, \text{m/s}}{3.38 \times 10^{-19} \, \text{J}} \][/tex]
3. Calculate the wavelength [tex]\(\lambda\)[/tex]:
[tex]\[ \lambda = \frac{1.9878 \times 10^{-25} \, \text{Js} \cdot \text{m/s}}{3.38 \times 10^{-19} \, \text{J}} \][/tex]
[tex]\[ \lambda = 5.881 \times 10^{-7} \, \text{m} \][/tex]
4. Convert the wavelength from meters to nanometers:
[tex]\[ 1 \, \text{m} = 10^9 \, \text{nm} \][/tex]
[tex]\[ \lambda = 5.881 \times 10^{-7} \, \text{m} \times 10^9 \, \text{nm/m} \][/tex]
[tex]\[ \lambda = 588.1 \, \text{nm} \][/tex]
5. Compare the calculated wavelength to the given choices:
- A. [tex]\(510 \, \text{nm}\)[/tex]
- B. [tex]\(460 \, \text{nm}\)[/tex]
- C. [tex]\(588 \, \text{nm}\)[/tex]
- D. [tex]\(416 \, \text{nm}\)[/tex]
The wavelength most closely matches option C: [tex]\(588 \, \text{nm}\)[/tex].
Therefore, the correct answer is:
C. [tex]\(588 \, \text{nm}\)[/tex]
[tex]\[ \lambda = \frac{h \cdot c}{E} \][/tex]
where:
- [tex]\(E\)[/tex] is the energy of the photon,
- [tex]\(h\)[/tex] is Planck's constant ([tex]\(6.626 \times 10^{-34}\)[/tex] joule seconds),
- [tex]\(c\)[/tex] is the speed of light ([tex]\(3.00 \times 10^8\)[/tex] meters per second).
Step-by-Step Solution:
1. Identify the given values:
- Energy [tex]\(E = 3.38 \times 10^{-19}\)[/tex] joules
- Planck's constant [tex]\(h = 6.626 \times 10^{-34}\)[/tex] joule seconds
- Speed of light [tex]\(c = 3.00 \times 10^8\)[/tex] meters per second
2. Plug the values into the wavelength formula:
[tex]\[ \lambda = \frac{6.626 \times 10^{-34} \, \text{Js} \times 3.00 \times 10^8 \, \text{m/s}}{3.38 \times 10^{-19} \, \text{J}} \][/tex]
3. Calculate the wavelength [tex]\(\lambda\)[/tex]:
[tex]\[ \lambda = \frac{1.9878 \times 10^{-25} \, \text{Js} \cdot \text{m/s}}{3.38 \times 10^{-19} \, \text{J}} \][/tex]
[tex]\[ \lambda = 5.881 \times 10^{-7} \, \text{m} \][/tex]
4. Convert the wavelength from meters to nanometers:
[tex]\[ 1 \, \text{m} = 10^9 \, \text{nm} \][/tex]
[tex]\[ \lambda = 5.881 \times 10^{-7} \, \text{m} \times 10^9 \, \text{nm/m} \][/tex]
[tex]\[ \lambda = 588.1 \, \text{nm} \][/tex]
5. Compare the calculated wavelength to the given choices:
- A. [tex]\(510 \, \text{nm}\)[/tex]
- B. [tex]\(460 \, \text{nm}\)[/tex]
- C. [tex]\(588 \, \text{nm}\)[/tex]
- D. [tex]\(416 \, \text{nm}\)[/tex]
The wavelength most closely matches option C: [tex]\(588 \, \text{nm}\)[/tex].
Therefore, the correct answer is:
C. [tex]\(588 \, \text{nm}\)[/tex]
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.