Question

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 6.99thz. calculate the wavelength of the infrared radiation. round your answer to 3 significant digits.

Explanation:

Step1: Convert frequency to Hz

Given frequency \( f = 6.99\ \text{THz}=6.99\times 10^{12}\ \text{Hz}\) (since \(1\ \text{THz} = 10^{12}\ \text{Hz}\)).

Step2: Use the formula \(c=\lambda f\)

The speed of light \(c = 3\times 10^{8}\ \text{m/s}\). Rearranging the formula for wavelength \(\lambda=\frac{c}{f}\).
Substitute \(c = 3\times 10^{8}\ \text{m/s}\) and \(f = 6.99\times 10^{12}\ \text{Hz}\) into the formula:
\(\lambda=\frac{3\times 10^{8}}{6.99\times 10^{12}}\ \text{m}\)

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Step3: Convert meters to micrometers

Since \(1\ \text{m}=10^{6}\ \mu\text{m}\), then \(\lambda = 0.429\times10^{-4}\times10^{6}\ \mu\text{m}\)

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Answer:

\(42.9\ \mu\text{m}\)