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Chapter 29: Problem 22

What are the wavelengths of (a) a \(100-\) MHz FM radio wave, (b) a 5.0 - GHz WiFi signal, (c) a 600 -THz light wave, and (d) a \(1.0-\) EHz X ray?

Short Answer

Expert verified
The wavelengths calculated are as such: a) The wavelength of the 100 -MHz FM radio wave is approximately 3 meters, b) The wavelength of the 5.0 - GHz WiFi signal is about 0.06 meters (or 6 centimeters), c) The wavelength of the 600 -THz light wave is roughly 500 nanometers, and d) The wavelength of the 1.0 - EHz X ray is about 0.3 nanometer.

Step by step solution

01

Calculate the wavelength of an FM radio wave

Given the frequency of the FM radio wave is \(100\) MHz, we will first convert this to Hz by multiplying by \(10^6\). So, \(ν = 100 \) MHz = \(100 \cdot 10^6\) Hz. From the formula \(C = λν\), we can solve for λ: λ = \(C ÷ ν\). Substituting the given values, \(C = 3.00 \cdot 10^8\) m/s and ν into the formula will give the wavelength of the FM radio wave.
02

Calculate the wavelength of a WiFi signal

Given the frequency of the WiFi signal is 5.0 GHz, we convert it to Hz by multiplying by \(10^9\). So, \(ν = 5.0 \) GHz = \(5.0 \cdot 10^9\) Hz. We then substitute into the formula λ = \(C ÷ ν\). This gives the wavelength of the WiFi signal.
03

Calculate the wavelength of a light wave

Given the frequency of the light wave is 600 THz, convert it to Hz by multiplying by \(10^{12}\). So, \(ν = 600 \) THz = \(600 \cdot 10^{12}\) Hz. Substituting into the formula, λ = \(C ÷ ν\), we get the wavelength of the light wave.
04

Calculate the wavelength of an X ray

Given the frequency of the X ray is 1.0 EHz, which is equivalent to \(1.0 × 10^{18}\) Hz. We can now substitute this into our formula, λ = \(C ÷ ν\), to acquire the wavelength of the X ray.

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Most popular questions from this chapter

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