To determine the frequency corresponding to an absorption line at a wavelength of 502 nm, we follow these steps:
1. Understand the relationship between wavelength and frequency:
The speed of light, [tex]\( c \)[/tex], is related to the frequency [tex]\( f \)[/tex] and wavelength [tex]\( \lambda \)[/tex] by the equation:
[tex]\[
c = f \cdot \lambda
\][/tex]
Rearranging this formula to solve for frequency, we get:
[tex]\[
f = \frac{c}{\lambda}
\][/tex]
2. Given values:
- Speed of light, [tex]\( c \)[/tex], is approximately [tex]\( 3.0 \times 10^{8} \)[/tex] meters per second (m/s).
- Wavelength, [tex]\( \lambda \)[/tex], is 502 nanometers (nm). We need to convert this to meters (m) for consistency in units.
[tex]\[
502 \, \text{nm} = 502 \times 10^{-9} \, \text{m}
\][/tex]
3. Calculate the frequency:
Substitute the given values into the frequency formula:
[tex]\[
f = \frac{3.0 \times 10^{8} \, \text{m/s}}{502 \times 10^{-9} \, \text{m}}
\][/tex]
Simplify the division:
[tex]\[
f = \frac{3.0 \times 10^{8}}{502 \times 10^{-9}}
\][/tex]
Perform the calculation:
[tex]\[
f = 5.97609561752988 \times 10^{14} \, \text{Hz}
\][/tex]
4. Match the frequency with the given options:
Among the given options, the frequency closest to our calculated value is:
[tex]\[
\boxed{5.98 \times 10^{14} \, \text{Hz}}
\][/tex]
So, the frequency corresponding to an absorption line at 502 nm is [tex]\( 5.98 \times 10^{14} \)[/tex] Hz, which corresponds to option C.
