Question

How to calculate the wavelength of a photon with a frequency of 71.6 THz

Answer 1

To calculate the wavelength of a photon given its frequency, you can use the equation that relates frequency (\( f \)) and wavelength (\( \lambda \)):

\[
\lambda = \frac{c}{f}
\]

where:
- \( \lambda \) is the wavelength,
- \( c \) is the speed of light in a vacuum (approximately \( 3.00 \times 10^8 \) meters per second),
- \( f \) is the frequency of the photon.

In this case, the frequency is given as \( 71.6 \) THz. First, we need to convert terahertz to hertz:

\[
71.6 \, \text{THz} = 71.6 \times 10^{12} \, \text{Hz}
\]

Now we can plug the values into the equation:

\[
\lambda = \frac{3.00 \times 10^8 \, \text{m/s}}{71.6 \times 10^{12} \, \text{Hz}}
\]

Calculating this gives:

\[
\lambda = \frac{3.00 \times 10^8}{71.6 \times 10^{12}} \approx 4.19 \times 10^{-6} \, \text{m}
\]

To express this in more convenient units, you might want to convert meters to nanometers (1 m = \( 10^9 \) nm):

\[
\lambda \approx 4.19 \times 10^{-6} \, \text{m} \times 10^9 \, \text{nm/m} \approx 4190 \, \text{nm}
\]

So the wavelength of a photon with a frequency of \( 71.6 \) THz is approximately \( 4190 \, \text{nm} \). Therefore, the answer is:

\[
\lambda \approx 4190 \, \text{nm}
\]