Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.
Sagot :
To determine which color of light corresponds to the photon with the given energy, we will follow these steps:
1. Calculate the Frequency of the Photon:
- The energy of a photon [tex]\(E\)[/tex] is given as [tex]\(3.38 \times 10^{-19} \, \text{J}\)[/tex].
- Planck's constant [tex]\(h\)[/tex] is given as [tex]\(6.63 \times 10^{-34} \, \text{J} \cdot \text{s}\)[/tex].
The relationship between the energy of a photon and its frequency [tex]\(f\)[/tex] is given by the formula:
[tex]\[ E = h \cdot f \][/tex]
Rearranging this formula to solve for frequency [tex]\(f\)[/tex]:
[tex]\[ f = \frac{E}{h} = \frac{3.38 \times 10^{-19} \, \text{J}}{6.63 \times 10^{-34} \, \text{J} \cdot \text{s}} = 5.098 \times 10^{14} \, \text{Hz} \][/tex]
2. Compare with the Provided Frequencies:
- Violet: [tex]\(7.59 \times 10^{14} \, \text{Hz}\)[/tex]
- Green: [tex]\(5.10 \times 10^{14} \, \text{Hz}\)[/tex]
- Yellow: [tex]\(5.01 \times 10^{14} \, \text{Hz}\)[/tex]
- Red: [tex]\(4.72 \times 10^{14} \, \text{Hz}\)[/tex]
3. Calculate the Absolute Differences:
- Difference with Violet:
[tex]\[ \left| 7.59 \times 10^{14} - 5.098 \times 10^{14} \right| = 2.492 \times 10^{14} \, \text{Hz} \][/tex]
- Difference with Green:
[tex]\[ \left| 5.10 \times 10^{14} - 5.098 \times 10^{14} \right| = 0.002 \times 10^{14} \, \text{Hz} = 2.0 \times 10^{12} \, \text{Hz} \][/tex]
- Difference with Yellow:
[tex]\[ \left| 5.01 \times 10^{14} - 5.098 \times 10^{14} \right| = 0.088 \times 10^{14} \, \text{Hz} = 8.8 \times 10^{12} \, \text{Hz} \][/tex]
- Difference with Red:
[tex]\[ \left| 4.72 \times 10^{14} - 5.098 \times 10^{14} \right| = 0.378 \times 10^{14} \, \text{Hz} = 37.8 \times 10^{12} \, \text{Hz} \][/tex]
4. Find the Minimum Difference:
- The smallest difference is with the frequency of Green light:
[tex]\[ 2.0 \times 10^{12} \, \text{Hz} \][/tex]
Therefore, the color of light that corresponds to the given photon is Green.
1. Calculate the Frequency of the Photon:
- The energy of a photon [tex]\(E\)[/tex] is given as [tex]\(3.38 \times 10^{-19} \, \text{J}\)[/tex].
- Planck's constant [tex]\(h\)[/tex] is given as [tex]\(6.63 \times 10^{-34} \, \text{J} \cdot \text{s}\)[/tex].
The relationship between the energy of a photon and its frequency [tex]\(f\)[/tex] is given by the formula:
[tex]\[ E = h \cdot f \][/tex]
Rearranging this formula to solve for frequency [tex]\(f\)[/tex]:
[tex]\[ f = \frac{E}{h} = \frac{3.38 \times 10^{-19} \, \text{J}}{6.63 \times 10^{-34} \, \text{J} \cdot \text{s}} = 5.098 \times 10^{14} \, \text{Hz} \][/tex]
2. Compare with the Provided Frequencies:
- Violet: [tex]\(7.59 \times 10^{14} \, \text{Hz}\)[/tex]
- Green: [tex]\(5.10 \times 10^{14} \, \text{Hz}\)[/tex]
- Yellow: [tex]\(5.01 \times 10^{14} \, \text{Hz}\)[/tex]
- Red: [tex]\(4.72 \times 10^{14} \, \text{Hz}\)[/tex]
3. Calculate the Absolute Differences:
- Difference with Violet:
[tex]\[ \left| 7.59 \times 10^{14} - 5.098 \times 10^{14} \right| = 2.492 \times 10^{14} \, \text{Hz} \][/tex]
- Difference with Green:
[tex]\[ \left| 5.10 \times 10^{14} - 5.098 \times 10^{14} \right| = 0.002 \times 10^{14} \, \text{Hz} = 2.0 \times 10^{12} \, \text{Hz} \][/tex]
- Difference with Yellow:
[tex]\[ \left| 5.01 \times 10^{14} - 5.098 \times 10^{14} \right| = 0.088 \times 10^{14} \, \text{Hz} = 8.8 \times 10^{12} \, \text{Hz} \][/tex]
- Difference with Red:
[tex]\[ \left| 4.72 \times 10^{14} - 5.098 \times 10^{14} \right| = 0.378 \times 10^{14} \, \text{Hz} = 37.8 \times 10^{12} \, \text{Hz} \][/tex]
4. Find the Minimum Difference:
- The smallest difference is with the frequency of Green light:
[tex]\[ 2.0 \times 10^{12} \, \text{Hz} \][/tex]
Therefore, the color of light that corresponds to the given photon is Green.
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.