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Chapter 28: Problem 14

It has been suggested that extraterrestrial civilizations would choose to communicate at a wavelength of \(21 \mathrm{~cm}\). Hydrogen atoms in interstellar space naturally emit at this wavelength, so astronomers studying the distribution of hydrogen around the Galaxy would already have their radio telescopes tuned to receive extraterrestrial signals. (a) Calculate the frequency of this radiation in megahertz. Is this inside or outside the water hole? (b) Discuss the merits of this suggestion.

Short Answer

Expert verified
The frequency of the radiation with a wavelength of 21cm is 1428.57 MHz, which falls within the water hole. The suggestion has several merits including expectation of tuning into this frequency by other civilizations, little absorption by cosmic gas and dust, and hydrogen's abundance.

Step by step solution

01

Understanding the wavelength and calculating the frequency

Firstly, it's important to transform the given wavelength from cm to meters because the constant speed of light (\( c \)) is commonly measured in meters per second. The given wavelength is 21 cm, which corresponds to 0.21 meters. We will also need the value of \( c \), the speed of light, which is approximately \( 3 × 10^8 \) m/s. Using the relation \( c = λf \), the frequency \( f \) can be found using the formula \( f = c / λ \). Substituting the values, we find \( f = (3 × 10^8) / 0.21 = 1.43 × 10^9 \) Hz.
02

Converting the frequency to megahertz

Hertz (Hz) is the SI unit of frequency, but in this exercise, we are asked to express the frequency in megahertz (MHz). To convert Hz to MHz, we divide the frequency in Hz by \( 10^6 \). Therefore, \( 1.43 × 10^9 Hz = 1.43 × 10^9 / 10^6 MHz = 1428.57 MHz \).
03

Checking if the frequency falls within the water hole.

The water hole in radio astronomy refers to the frequency range between 1420 MHz and 1666 MHz. Looking at the calculated frequency of 1428.57 MHz, it is clear that this falls within the water hole.
04

Discussion of the merits of this suggestion

There are several solid arguments to support the suggestion. Firstly, since the hydrogen line lies in the range of the water hole, human astronomers will already have their radio telescopes tuned for these signals. This increases the chance of picking up extraterrestrial signals if they are being sent. Secondly, hydrogen is the most abundant element in the universe; an extraterrestrial civilization might quite naturally pick this line for communication, expecting that other civilizations would be observing it. Lastly, signals at this frequency can pass through galactic and intergalactic gas and dust with little absorption.

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