Infrared radiation from young stars can pass through the heavy dust clouds surrounding them, allowing astronomers here on Earth to study the earliest stages of star formation, before a star begins to emit visible light. Suppose an infrared telescope is tuned to detect infrared radiation with a frequency of 7.65THz. Calculate the wavelength of the infrared radiation.
Round your answer to  significant digits.


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.

Infrared radiation from young stars can pass through the heavy dust clouds surrounding them, allowing astronomers here on Earth to study the earliest stages of star formation, before a star begins to emit visible light. Suppose an infrared telescope is tuned to detect infrared radiation with a frequency of 7.65THz. Calculate the wavelength of the infrared radiation. Round your answer to significant digits.

Learn how to calculate the wavelength of infrared radiation detected by a telescope, tuned to a frequency of 7.65 THz. This problem involves the wave equation and is suitable for students in Grades 10-12. Understand the relationship between frequency and wavelength with a step-by-step solution.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation