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Chapter 8: Problem 127

For electromagnetic radiation transmitted through a vacuum, state whether each of the following properties is directly proportional to, inversely proportional to, or independent of the frequency: (a) velocity; (b) wavelength; (c) energy per mole. Explain.

Short Answer

Expert verified
a) Velocity is independent of frequency. b) Wavelength is inversely proportional to frequency. c) Energy per mole is directly proportional to frequency.

Step by step solution

01

Analyzing the relationship with velocity

For electromagnetic radiation traveling through a vacuum, the velocity, often represented by 'c', is constant regardless of its frequency. 'c' stands for the speed of light in vacuum, which is always 3.0 x 10^8 m/s. Hence, the frequency is independent of the velocity.
02

Analyzing the relationship with wavelength

The wavelength, often denoted by 'λ', of electromagnetic radiation is inversely proportional to its frequency. This fact can be understood by the wave equation, c=\( \lambda \cdot \nu \), where \( \nu \) is frequency. As c is constant, if \( \nu \) increases, \( \lambda \) decreases and vice-versa.
03

Analyzing the relationship with energy per mole

The energy of electromagnetic radiation is directly proportional to its frequency. This relationship is denoted by Planck's equation, E=h \cdot \( \nu \), where h is Planck's constant. As the frequency \( \nu \) increases, energy E also increases, therefore they are directly proportional. To find energy per mole, multiply energy of one photon with Avogadro's number (6.022 x 10^23). As both the elements being multiplied are directly proportional to frequency, energy per mole is also directly proportional to frequency.

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Most popular questions from this chapter

A molecule of chlorine can be dissociated into atoms by absorbing a photon of sufficiently high energy. Any excess energy is translated into kinetic energy as the atoms recoil from one another. If a molecule of chlorine at rest absorbs a photon of 300 nm wavelength, what will be the velocity of the two recoiling atoms? Assume that the excess energy is equally divided between the two atoms. The bond energy of \(\mathrm{Cl}_{2}\) is \(242.6 \mathrm{kJ} \mathrm{mol}^{-1}\)

On the basis of the periodic table and rules for electron configurations, indicate the number of (a) \(2 p\) electrons in \(\mathrm{N} ;\) (b) \(4 \mathrm{s}\) electrons in \(\mathrm{Rb} ;\) (c) \(4 \mathrm{d}\) electrons in As; (d) \(4 f\) electrons in \(\mathrm{Au} ;\) (e) unpaired electrons in \(\mathrm{Pb} ;\) (f) elements in group 14 of the periodic table; (g) elements in the sixth period of the periodic table.

What are the (a) frequency, in \(s^{-1}\), and (b) wavelength, in nanometers, of the light emitted when the electron in a hydrogen atom drops from the energy level \(n=7\) to \(n=4 ?\) (c) In what portion of the electromagnetic spectrum is this light?

In what region of the electromagnetic spectrum would you expect to find radiation having an energy per photon 100 times that associated with 988 nm radiation?

The following electron configurations correspond to the ground states of certain elements. Name each element. (a) \([\mathrm{Rn}] 7 s^{2} 6 d^{2} ;\) (b) \([\mathrm{He}] 2 s^{2} 2 p^{2} ;\) (c) \([\mathrm{Ar}] 3 d^{3} 4 s^{2}\) (d) \([\mathrm{Kr}] 4 d^{10} 5 s^{2} 5 p^{4} ;\) (e) \([\mathrm{Xe}] 4 f^{2} 6 s^{2} 6 p^{1}\)
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