Question
What is the wavelength of yellow light with the frequency of 5.09e14
Answers
GPT-4o mini
To find the wavelength of light, you can use the formula:
\[
\lambda = \frac{c}{f}
\]
where:
- \(\lambda\) is the wavelength,
- \(c\) is the speed of light (approximately \(3.00 \times 10^8\) meters per second),
- \(f\) is the frequency.
Given that the frequency \(f = 5.09 \times 10^{14}\) Hz, we can substitute the values into the formula:
\[
\lambda = \frac{3.00 \times 10^8 \, \text{m/s}}{5.09 \times 10^{14} \, \text{Hz}}
\]
Calculating this gives:
\[
\lambda \approx \frac{3.00 \times 10^8}{5.09 \times 10^{14}} \approx 5.89 \times 10^{-7} \, \text{meters}
\]
To convert this into nanometers (1 nm = \(10^{-9}\) m):
\[
\lambda \approx 5.89 \times 10^{-7} \, \text{m} = 589 \, \text{nm}
\]
So, the wavelength of yellow light with a frequency of \(5.09 \times 10^{14}\) Hz is approximately **589 nm**.
\[
\lambda = \frac{c}{f}
\]
where:
- \(\lambda\) is the wavelength,
- \(c\) is the speed of light (approximately \(3.00 \times 10^8\) meters per second),
- \(f\) is the frequency.
Given that the frequency \(f = 5.09 \times 10^{14}\) Hz, we can substitute the values into the formula:
\[
\lambda = \frac{3.00 \times 10^8 \, \text{m/s}}{5.09 \times 10^{14} \, \text{Hz}}
\]
Calculating this gives:
\[
\lambda \approx \frac{3.00 \times 10^8}{5.09 \times 10^{14}} \approx 5.89 \times 10^{-7} \, \text{meters}
\]
To convert this into nanometers (1 nm = \(10^{-9}\) m):
\[
\lambda \approx 5.89 \times 10^{-7} \, \text{m} = 589 \, \text{nm}
\]
So, the wavelength of yellow light with a frequency of \(5.09 \times 10^{14}\) Hz is approximately **589 nm**.