Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

Assume that lasers are available whose wavelengths can be precisely “tuned” to anywhere in the visible range—that is, in the range $450 nm < λ < 650 nm$ . If every television channel occupies a bandwidth of 10 MHz, how many channels can be accommodated within this wavelength range?

There can be $2.1 \times 10^{7}$ channels accommodated within this wavelength range.

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: The given data:

a) Wavelength range of the visible region, $450 nm < λ < 650 nm$

b) Bandwidth of the television channel, $Δ f = 10 MHz$

Step 2: Understanding the concept of bandwidth frequency

Using the formula of energy due to Planck's relation, we can get the energy difference value of the states. Now, for the corresponding energy difference between the two states, we can consider the energy difference between the states of the hydrogen atom n = 1 and n = 2 to compare the difference value.

Formula:

The frequency of a wave,

$f = \frac{c}{λ}$ ….. (1)

Here, $λ$ is the wavelength.

Speed of light, $c = 3 \times 10^{8} \frac{m}{s}$

Step 3: Calculation of accommodated channels within the visible region:

Let, the range of frequency of the microwave be $∆ f$ .

Then, the number of channels that could be accommodated within the range can be given as follow.

$N = \frac{∆ f}{10 M e V} = \frac{1}{10^{7} e V} (\frac{3 \times 10^{8} m / s}{450 \times 10^{- 9} m} - \frac{3 \times 10^{8} m / s}{650 \times 10^{- 9} m}) = 6.7 \times 10^{7} - 4.6 \times 10^{7} = 2.1 \times 10^{7} channels$

$N = 21.0 \times 10^{6} channels = 21.0 million channels$

Hence, the number channels accommodated is $2.1 \times 10^{7}$ .

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Fundamentals Of Physics

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Short Answer

Assume that lasers are available whose wavelengths can be precisely “tuned” to anywhere in the visible range—that is, in the range $450 nm < λ < 650 nm$ . If every television channel occupies a bandwidth of 10 MHz, how many channels can be accommodated within this wavelength range?

Step by Step Solution

Step 1: The given data:

Step 2: Understanding the concept of bandwidth frequency

Step 3: Calculation of accommodated channels within the visible region:

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Short Answer

Assume that lasers are available whose wavelengths can be precisely “tuned” to anywhere in the visible range—that is, in the range 450 nm<λ<650 nm . If every television channel occupies a bandwidth of 10 MHz, how many channels can be accommodated within this wavelength range?

Step by Step Solution

Step 1: The given data:

Step 2: Understanding the concept of bandwidth frequency

Step 3: Calculation of accommodated channels within the visible region:

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Assume that lasers are available whose wavelengths can be precisely “tuned” to anywhere in the visible range—that is, in the range $450 nm < λ < 650 nm$ . If every television channel occupies a bandwidth of 10 MHz, how many channels can be accommodated within this wavelength range?