To find which color of light corresponds to the given photon energy, we use the relationship between the energy ([tex]\(E\)[/tex]) of a photon, its frequency ([tex]\(f\)[/tex]), and Planck's constant ([tex]\(h\)[/tex]). The formula is:
[tex]\[ E = h \cdot f \][/tex]
Given:
- Energy of the photon ([tex]\(E\)[/tex]) = [tex]\(3.38 \times 10^{-19} \, J\)[/tex]
- Planck's constant ([tex]\(h\)[/tex]) = [tex]\(6.63 \times 10^{-34} \, J \cdot s\)[/tex]
We need to find the frequency ([tex]\(f\)[/tex]) of the photon:
[tex]\[ f = \frac{E}{h} = \frac{3.38 \times 10^{-19}}{6.63 \times 10^{-34}} \][/tex]
Calculating the frequency:
[tex]\[ f \approx 5.10 \times 10^{14} \, Hz \][/tex]
Now, we compare this frequency to the frequencies of different colors of light provided:
1. Violet: [tex]\(7.59 \times 10^{14} \, Hz\)[/tex]
2. Green: [tex]\(5.10 \times 10^{14} \, Hz\)[/tex]
3. Yellow: [tex]\(5.01 \times 10^{14} \, Hz\)[/tex]
4. Red: [tex]\(4.72 \times 10^{14} \, Hz\)[/tex]
The frequency we calculated [tex]\(5.10 \times 10^{14} \, Hz\)[/tex] matches the frequency of green light. Therefore, the color of the light corresponding to the photon is green.
