(a)
The number of components and the wavelength of each components.
(a)
Answer to Problem 56P
The numbers of components are
The wavelengths of each component are
Explanation of Solution
Write the expression for the separation distance.
Here,
Write the expression for the used wavelength.
Here,
Rewrite the expression (I) in terms of the number of components by using (II).
Rewrite the equation (I) in terms of wavelength.
Conclusion:
Substitute,
Hence, the number of components will be 1110100, 1110101, 1110102, 1110103 and so on.
For the first wavelength:
Substitute,
For the second wavelength:
Substitute,
For the third wavelength:
Substitute,
For the fourth wavelength:
Substitute,
Hence only first three wavelengths are possible.
Thus, the numbers of components are only three and the wavelengths of each components are
(b)
The root mean square speed for neon atom.
(b)
Answer to Problem 56P
The root mean square speed for neon atom is
Explanation of Solution
Write the expression for the root mean square speed by using conservation of energy.
Here,
Conclusion:
Substitute,
Thus, the root mean square speed for neon atom is
(c)
Whether the Doppler Effect for light emission by moving neon atoms should realistically make the bandwidth of the light amplifier larger than the 0.00140nm at
(c)
Answer to Problem 56P
The Doppler Effect for light emission by moving neon atoms should realistically make the bandwidth of the light amplifier larger than the 0.00140nm at
Explanation of Solution
Write the expression for the frequency from Doppler Effect.
Here,
Since, the frequency and the wavelength is inversely proportional, the apparent wavelength equation can be calculated by using equation (VI).
Write the expression for the apparent wavelength by using (II).
Here,
Conclusion:
Substitute,
The calculated wavelength is beyond limit. There will be many atoms which are moving more than rms speed. Hence, it can be expected that there will be more Doppler broadening of the resonance amplification peak.
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Chapter 24 Solutions
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