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.
