Certainly! To determine the frequency of yellow-green light with a wavelength of 550 nm, we can use the formula that relates the speed of light, the wavelength, and the frequency. The formula is:
[tex]\[ \text{frequency} = \frac{\text{speed of light}}{\text{wavelength}} \][/tex]
Here is the step-by-step solution to find the frequency:
1. Identify the given values:
- Wavelength ([tex]\(\lambda\)[/tex]) = 550 nanometers (nm)
- Speed of light ([tex]\(c\)[/tex]) = [tex]\(3.0 \times 10^8\)[/tex] meters per second (m/s)
2. Convert the wavelength from nanometers to meters:
- [tex]\(1 \, \text{nm} = 10^{-9} \, \text{m}\)[/tex]
- [tex]\[ 550 \, \text{nm} = 550 \times 10^{-9} \, \text{m} \][/tex]
- [tex]\[ 550 \times 10^{-9} \, \text{m} = 5.5 \times 10^{-7} \, \text{m} \][/tex]
3. Use the formula to calculate the frequency:
- [tex]\[ \text{frequency} = \frac{c}{\lambda} \][/tex]
- [tex]\[ \text{frequency} = \frac{3.0 \times 10^8 \, \text{m/s}}{5.5 \times 10^{-7} \, \text{m}} \][/tex]
4. Perform the division:
- [tex]\[ \frac{3.0 \times 10^8}{5.5 \times 10^{-7}} = 5.4545454545454544 \times 10^{14} \, \text{Hz} \][/tex]
Therefore, the frequency of yellow-green light with a wavelength of 550 nm is approximately [tex]\(5.45 \times 10^{14} \, \text{Hz}\)[/tex].
Given the options, the closest match is:
O [tex]\(5.5 \times 10^{14} \, \text{Hz}\)[/tex]
So the correct answer is [tex]\(5.5 \times 10^{14} \, \text{Hz}\)[/tex].
