To determine the frequency that corresponds to an absorption line at [tex]\( 527 \, \text{nm} \)[/tex], follow these steps:
1. Understand the relationship between wavelength and frequency:
- The speed of light ([tex]\( c \)[/tex]) is approximately [tex]\( 3 \times 10^8 \, \text{m/s} \)[/tex].
- The formula to relate wavelength ([tex]\( \lambda \)[/tex]) and frequency ([tex]\( f \)[/tex]) is:
[tex]\[
f = \frac{c}{\lambda}
\][/tex]
2. Convert the wavelength from nanometers to meters:
- The given wavelength is [tex]\( 527 \, \text{nm} \)[/tex]. Since [tex]\( 1 \, \text{nm} = 10^{-9} \, \text{m} \)[/tex]:
[tex]\[
527 \, \text{nm} = 527 \times 10^{-9} \, \text{m}
\][/tex]
3. Calculate the frequency:
- Using the speed of light ([tex]\( c \)[/tex]) and the converted wavelength ([tex]\( \lambda \)[/tex]), the frequency ([tex]\( f \)[/tex]) is calculated as:
[tex]\[
f = \frac{3 \times 10^8 \, \text{m/s}}{527 \times 10^{-9} \, \text{m}}
\][/tex]
4. Compare the calculated frequency with the given choices:
- The calculated frequency should be compared with the following given choices:
- [tex]\(\text{A. } 1.76 \times 10^{14} \, \text{Hz}\)[/tex]
- [tex]\(\text{B. } 5.69 \times 10^{14} \, \text{Hz}\)[/tex]
- [tex]\(\text{C. } 6.71 \times 10^{14} \, \text{Hz}\)[/tex]
- [tex]\(\text{D. } 3.77 \times 10^{14} \, \text{Hz}\)[/tex]
After going through these steps, we find that none of the given choices match the calculated frequency closely. Therefore, the correct answer to this question is:
[tex]\[
0 \quad \text{(indicating no match found)}
\][/tex]
Thus, the frequency that corresponds to an absorption line at [tex]\( 527 \, \text{nm} \)[/tex] does not match any of the given choices.
