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Chapter 6: Problem 16

Determine which of the following statements are false and correct them. (a) The frequency of radiation increases as the wavelength increases. (b) Electromagnetic radiation travels through a vacuum at a constant speed, regardless of wavelength. (c) Infrared light has higher frequencies than visible light. (d) The glow from a fireplace, the energy within a microwave oven, and a foghorn blast are all forms of electromagnetic radiation.

Short Answer

Expert verified
(a) False. Corrected: The frequency of radiation decreases as the wavelength increases. (b) True. (c) False. Corrected: Infrared light has lower frequencies than visible light. (d) Partially true. Corrected: The glow from a fireplace and the energy within a microwave oven are forms of electromagnetic radiation, while a foghorn blast is not.

Step by step solution

01

Statement (a) Analysis

The frequency of radiation increases as the wavelength increases. This statement claims that the frequency of electromagnetic radiation is directly proportional to the wavelength. However, from the formula for the speed of light, we know that the frequency is inversely proportional to the wavelength: \(c = \lambda\nu\) where c is the speed of light, λ is the wavelength, and ν is the frequency.
02

Statement (a) Correction

The frequency of radiation decreases as the wavelength increases.
03

Statement (b) Analysis

Electromagnetic radiation travels through a vacuum at a constant speed, regardless of wavelength. This statement is true. The speed of electromagnetic radiation in a vacuum remains constant, which is approximately 3 x 10^8 meters per second (the speed of light), regardless of wavelength.
04

Statement (c) Analysis

Infrared light has higher frequencies than visible light. This statement is incorrect. Infrared light has lower frequencies than visible light. The electromagnetic spectrum is ordered from low frequencies to high frequencies, with the order being radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays.
05

Statement (c) Correction

Infrared light has lower frequencies than visible light.
06

Statement (d) Analysis

The glow from a fireplace, the energy within a microwave oven, and a foghorn blast are all forms of electromagnetic radiation. This statement is partially true. The glow from a fireplace and the energy within a microwave oven are both forms of electromagnetic radiation in the infrared and microwave range, respectively. However, a foghorn blast is a form of sound wave, which is not part of the electromagnetic spectrum.
07

Statement (d) Correction

The glow from a fireplace and the energy within a microwave oven are forms of electromagnetic radiation, while a foghorn blast is not.

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Most popular questions from this chapter

The visible emission lines observed by Balmer all involved $n_{\mathrm{f}}=2 .$ (a) Which of the following is the best explanation of why the lines with \(n_{\mathrm{f}}=3\) are not observed in the visible portion of the spectrum: (i) Transitions to \(n_{\mathrm{f}}=3\) are not allowed to happen, (ii) transitions to \(n_{\mathrm{f}}=3\) emit photons in the infrared portion of the spectrum, (iii) transitions to \(n_{\mathrm{f}}=3\) emit photons in the ultraviolet portion of the spectrum, or (iv) transitions to \(n_{\mathrm{f}}=3\) emit photons that are at exactly the same wavelengths as those to \(n_{\mathrm{f}}=2 .\) (b) Calculate the wavelengths of the first three lines in the Balmer series-those for which \(n_{1}=3,4\), and 5 -and identify these lines in the emission spectrum shown in Figure 6.11

(a) What is the frequency of radiation whose wavelength is $0.86 \mathrm{nm} ?(\mathbf{b})$ What is the wavelength of radiation that has a frequency of \(6.4 \times 10^{11} \mathrm{~s}^{-1} ?(\mathbf{c})\) Would the radiations in part (a) or part (b) be detected by an X-ray detector? (d) What distance does electromagnetic radiation travel in 0.38 ps?

An experiment called the Stern-Gerlach experiment helped establish the existence of electron spin. In this experiment, a beam of silver atoms is passed through a magnetic field, which deflects half of the silver atoms in one direction and half in the opposite direction. The separation between the two beams increases as the strength of the magnetic field increases. (a) What is the electron configuration for a silver atom? (b) Would this experiment work for a beam of cadmium (Cd) atoms? (c) Would this experiment work for a beam of fluorine (F) atoms?

(a) For an He+ ion, do the \(2 s\) and \(2 p\) orbitals have the same energy? If not, which orbital has a lower energy? (b) If we add one electron to form the He atom, would your answer to part (a) change?

(a) Calculate the energy of a photon of electromagnetic radiation whose frequency is \(2.94 \times 10^{14} \mathrm{~s}^{-1}\). (b) Calculate the energy of a photon of radiation whose wavelength is 413 \(\mathrm{nm} .\) (c) What wavelength of radiation has photons of energy $6.06 \times 10^{-19} \mathrm{~J} ?$
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