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Chapter 4: Problem 42

Suppose a radio wave has a wavelength of \(10 \mathrm{~m}\). What is the energy of this radiation (in joules)?

Short Answer

Expert verified
The energy of the radio wave with a wavelength of 10 meters is approximately 1.99 x 10^-26 joules.

Step by step solution

01

1. Calculate the Frequency

We are given the wavelength (λ) and need to find the frequency (f). We can use the speed of light (c) formula to calculate the frequency: c = λf Here, c is the speed of light which is approximately 3 x 10^8 meters per second (m/s), and λ is the wavelength which is 10 meters. Rearranging the formula, we can solve for frequency: f = c/λ
02

2. Substitute the values and find the Frequency (f)

Now that we have the frequency formula (f = c/λ), we can substitute the values of the speed of light (c) and the wavelength (λ). f = (3 x 10^8 m/s) / (10 m)
03

3. Calculate the Frequency (f)

Simplify the expression to find the frequency of the radio wave: f = 3 x 10^7 s^-1 The frequency (f) of the radio wave is 3 x 10^7 s^-1.
04

4. Calculate the Energy of a wave (E)

Now we have the frequency (f). We can use the second formula to calculate the energy of this radiation. E = hf Planck's constant (h) is approximately 6.63 x 10^-34 Js.
05

5. Substitute the values and find the Energy (E)

Now that we have the energy formula (E = hf), we can substitute the values of Planck's constant (h) and the frequency (f). E = (6.63 x 10^-34 Js) * (3 x 10^7 s^-1)
06

6. Calculate the Energy of the radio wave (E)

Simplify the expression to find the energy of the radio wave: E = 1.99 x 10^-26 J The energy of the radio wave with a wavelength of 10 meters is approximately 1.99 x 10^-26 joules.

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