To calculate the frequency of visible light given a wavelength of 464.1 nm, we can use the relationship between the speed of light, wavelength, and frequency. The formula we use is:
[tex]\[ \text{frequency} = \frac{\text{speed of light}}{\text{wavelength}} \][/tex]
Here are the detailed steps to solve the problem:
1. Convert the wavelength from nanometers to meters:
[tex]\[ \text{wavelength (in meters)} = 464.1 \, \text{nm} \times 10^{-9} \, \text{m/nm} \][/tex]
[tex]\[ \text{wavelength (in meters)} = 464.1 \times 10^{-9} \, \text{m} \][/tex]
[tex]\[ \text{wavelength (in meters)} = 4.641 \times 10^{-7} \, \text{m} \][/tex]
2. Use the known speed of light in a vacuum:
[tex]\[ \text{speed of light} = 3.0 \times 10^8 \, \text{m/s} \][/tex]
3. Calculate the frequency using the formula:
[tex]\[ \text{frequency} = \frac{3.0 \times 10^8 \, \text{m/s}}{4.641 \times 10^{-7} \, \text{m}} \][/tex]
4. Perform the division to find the frequency:
[tex]\[ \text{frequency} \approx 6.464 \times 10^{14} \, \text{s}^{-1} \][/tex]
Therefore, the frequency of visible light with a wavelength of 464.1 nm is approximately [tex]\( 6.460 \times 10^{14} \, \text{s}^{-1} \)[/tex]. This corresponds to the third option in the given choices:
[tex]\[ 6.460 \times 10^{14} \, \text{s}^{-1} \][/tex]
