Question

question 18
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 detector is tuned to detect infrared radiation with a frequency of 17.7 thz. calculate the wavelength of the infrared radiation. be sure your answer has the correct number of significant digits.

Explanation:

Step1: Recall the wave - speed formula

The speed of light $c = \lambda f$, where $c = 3.00\times10^{8}\ m/s$ is the speed of light in a vacuum, $\lambda$ is the wavelength, and $f$ is the frequency. We need to solve for $\lambda$, so $\lambda=\frac{c}{f}$.

Step2: Convert the frequency to SI units

The given frequency $f = 17.7\ THz=17.7\times10^{12}\ Hz$.

Step3: Calculate the wavelength

Substitute $c = 3.00\times10^{8}\ m/s$ and $f = 17.7\times10^{12}\ Hz$ into the formula $\lambda=\frac{c}{f}$.
$\lambda=\frac{3.00\times 10^{8}}{17.7\times 10^{12}}=\frac{3.00}{17.7}\times10^{- 4}\ m$.
$\lambda\approx1.69\times10^{-5}\ m$ (rounded to three significant digits).

Answer:

$1.69\times 10^{-5}\ m$