To calculate the wavelength of the infrared radiation, we can use the equation that relates the speed of light ($c$), frequency ($f$), and wavelength ($\lambda$):

$\lambda = \frac{c}{f}$

Where:

• $c$ is the speed of light in a vacuum, approximately $3.00 \times 10^8$ meters per second (m/s).
• $f$ is the frequency of the radiation.

Given:

• $f = 7.65 \, \text{THz} = 7.65 \times 10^{12} \, \text{Hz}$

Now, we can plug in the values:

$\lambda = \frac{3.00 \times 10^8 \, \text{m/s}}{7.65 \times 10^{12} \, \text{Hz}}$

Let's calculate this.

$\lambda = \frac{3.00 \times 10^8}{7.65 \times 10^{12}} \approx 3.92 \times 10^{-5} \, \text{m}$

So, the wavelength of the infrared radiation is approximately 39.2 micrometers (µm).

Would you like more details or have any questions? Here are 5 related questions:

1. How does the wavelength of radiation affect its ability to pass through dust clouds?
2. What is the relationship between frequency and energy of radiation?
3. How do astronomers use infrared telescopes to study star formation?
4. What is the range of wavelengths for infrared radiation?
5. Why can't visible light pass through the dust clouds as effectively as infrared radiation?

Tip: Remember, shorter wavelengths correspond to higher frequencies and energies, which affects how radiation interacts with matter.