IDNLearn.com connects you with a community of knowledgeable individuals ready to help. Our Q&A platform is designed to provide quick and accurate answers to any questions you may have.
Sagot :
To find the frequency of light with a given wavelength, we can use the formula that relates the speed of light ([tex]\(c\)[/tex]), frequency ([tex]\(f\)[/tex]), and wavelength ([tex]\(\lambda\)[/tex]):
[tex]\[ c = \lambda \times f \][/tex]
Here:
- The speed of light [tex]\(c\)[/tex] in a vacuum is approximately [tex]\(3 \times 10^8\)[/tex] meters per second.
- The wavelength [tex]\(\lambda\)[/tex] is given as 523 nanometers (nm). We need to convert this into meters by multiplying by [tex]\(10^{-9}\)[/tex], since 1 nm = [tex]\(10^{-9}\)[/tex] meters.
Let's write the steps clearly:
1. Convert the wavelength into meters:
[tex]\[ \lambda = 523 \, \text{nm} \times 10^{-9} \, \frac{\text{meters}}{\text{nm}} = 523 \times 10^{-9} \, \text{meters} \][/tex]
2. Rearrange the formula to solve for frequency [tex]\(f\)[/tex]:
[tex]\[ f = \frac{c}{\lambda} \][/tex]
3. Substitute the values into the formula:
[tex]\[ f = \frac{3 \times 10^8 \, \text{meters/second}}{523 \times 10^{-9} \, \text{meters}} \][/tex]
4. Calculate the frequency:
[tex]\[ f \approx 573613766730401.5 \, \text{Hz} \][/tex]
The result is:
[tex]\[ f \approx 5.74 \times 10^{14} \, \text{Hz} \][/tex]
Given the options:
A) 5.74 x 104Hz
B) 6.58 x 10 Hz
C) 6.58 x 104Hz
D) 5.74 x 10 Hz
It seems there is a typo or error in the question since none of the provided options match the correct frequency value of approximately [tex]\(5.74 \times 10^{14}\)[/tex] Hz.
The correct answer should be around [tex]\(5.74 \times 10^{14}\)[/tex] Hz.
[tex]\[ c = \lambda \times f \][/tex]
Here:
- The speed of light [tex]\(c\)[/tex] in a vacuum is approximately [tex]\(3 \times 10^8\)[/tex] meters per second.
- The wavelength [tex]\(\lambda\)[/tex] is given as 523 nanometers (nm). We need to convert this into meters by multiplying by [tex]\(10^{-9}\)[/tex], since 1 nm = [tex]\(10^{-9}\)[/tex] meters.
Let's write the steps clearly:
1. Convert the wavelength into meters:
[tex]\[ \lambda = 523 \, \text{nm} \times 10^{-9} \, \frac{\text{meters}}{\text{nm}} = 523 \times 10^{-9} \, \text{meters} \][/tex]
2. Rearrange the formula to solve for frequency [tex]\(f\)[/tex]:
[tex]\[ f = \frac{c}{\lambda} \][/tex]
3. Substitute the values into the formula:
[tex]\[ f = \frac{3 \times 10^8 \, \text{meters/second}}{523 \times 10^{-9} \, \text{meters}} \][/tex]
4. Calculate the frequency:
[tex]\[ f \approx 573613766730401.5 \, \text{Hz} \][/tex]
The result is:
[tex]\[ f \approx 5.74 \times 10^{14} \, \text{Hz} \][/tex]
Given the options:
A) 5.74 x 104Hz
B) 6.58 x 10 Hz
C) 6.58 x 104Hz
D) 5.74 x 10 Hz
It seems there is a typo or error in the question since none of the provided options match the correct frequency value of approximately [tex]\(5.74 \times 10^{14}\)[/tex] Hz.
The correct answer should be around [tex]\(5.74 \times 10^{14}\)[/tex] Hz.
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Your search for solutions ends here at IDNLearn.com. Thank you for visiting, and come back soon for more helpful information.