Chapter 3

Why are the various forms of radiant energy called electromagnetic radiation?

Dental X-Rays When X-ray images are taken of your tecth and gums in the dentist's office, your body is covered with a lead shield. Explain the need for this precaution.

Lava As hot molten lava cools, it begins to solidify and no longer glows in the dark. Does this mean it no longer emits any kind of electromagnetic radiation? If not, what kind of radiation is it likely to emit once it is no longer "red" hot?

If light consists of waves, why don't objects look "wavy" to us?

Submarine Communications The Russian and American navies developed extremely low-frequency communications networks to send messages to submerged submarines. The frequency of the carrier wave of the Russian network was \(82 \mathrm{Hz},\) while the Americans used \(76 \mathrm{Hz}\) a. What was the ratio of the wavelengths of the Russian network to the American network? b. To calculate the actual underwater wavelength of the transmissions in either network, what additional information would you need?

Broadcast Frequencies FM radio stations broadcast in a band of frequencies between 88 and 108 megahertz (MHz). Calculate the wavelengths corresponding to the broadcast frequencies of the following radio stations: a. KRNU (Lincoln, NE), 90.3 MHz b. WBRU (Providence, RI), \(95.5 \mathrm{MHz}\) c. WYLD (New Orleans, LA), 98.5 MHz d. WAAF (Boston, MA), \(107.3 \mathrm{MHz}\)

In 1895 German physicist Wilhclm Röntgen discovered X-rays. He also discovered that X-rays emitted by different metals have different wavelengths. Which X-rays have the higher frequency, those emitted by (a) Cu \((\lambda=0.154 \mathrm{nm})\) or (b) iron \((\lambda=194 \mathrm{pm}) ?\)

Garage Door Openers The remote control units for garage door openers transmit electromagnetic radiation. Before 2005 they operated on a frequency of \(390 \mathrm{MHz}\), but since 2005, the operating wavelength has been 952 mm. Which radiation has the lower frequency, the pre-2005 or the post- 2005 devices?

Speed of Light How long does it take light to reach Earth from the sun when the distance between them is 149.6 million kilometers?

Exploration of the Solar System The Voyager 1 spacecraft was launched in 1977 to explore the outer solar system and interstellar space. By December 2012 , it was \(1.85 \times 10^{10} \mathrm{km}\) from Earth and still sending and receiving data. How long did it take a signal from Earth to reach Voyager 1 over this distance?

Describe the similarities and differences in the atomic emission and absorption spectra of an element.

Are the Fraunhofer lines the result of atomic emission or atomic absorption?

How did the study of the atomic emission spectra of the elements lead to the identification of the origins of the Fraunhofer lines in sunlight?

What is a quantum?

What is a photon?

If a piece of tungsten metal were heated to \(1000 \mathrm{K},\) would it emit light in the dark? If so, what color?

Incandescent Lightbulbs A variable power supply is connected to an incandescent lightbulb. At the lowest power setting, the bulb feels warm to the touch but produces no light. At medium power, the lightbulb filament emits a red glow. At the highest power, the lightbulb emits white light. Explain this emission pattern.

Tanning Booths Prolonged exposure to ultraviolet radiation in tanning booths significantly increases the risk of skin cancer. What is the energy of a photon of UV light with a wavelength of \(3.00 \times 10^{-7} \mathrm{m} ?\)

Which of the following have quantized valucs? Explain your selections. a. The elevation of the treads of a moving escalator b. The elevations at which the doors of an elevator open c. The specd of an automobile

Which of the following have quantized values? Explain your selections. a. The pitch of a note played on a slide trombone b. The pitch of a note played on a flute c. The wavelengths of light produced by the heating elements in a toaster d. The wind speed at the top of Mt. Everest

The first ionization energy of a gas-phase atom of a particular element is \(6.24 \times 10^{-19} \mathrm{J} .\) What is the maximum wavelength of electromagnetic radiation that could ionize this atom?

Solar Power Photovoltaic cells convert solar energy into electricity. Could germanium \(\left(\Phi=7.21 \times 10^{-19} \mathrm{J}\right)\) be used to convert visible sunlight to electricity? Assume that most of the electromagnetic energy from the sun in the visible region is at wavelengths shorter than \(600 \mathrm{nm}\).

With reference to Problem \(3.41,\) could tin \((\Phi=6.20 \times\) \(\left.10^{-19} \mathrm{J}\right)\) be used to construct solar cells?

Titanium \(\left(\Phi=6.94 \times 10^{-19} \mathrm{J}\right)\) and silicon \((\Phi=7.24 \times\) \(\left.10^{-19} \mathrm{J}\right)\) surfaces are irradiated with UV radiation with a wavelength of \(250 \mathrm{nm}\). Which surface emits clectrons with the longer wavelength? What is the wavelength of the electrons emitted by the titanium surface?

Red Lasers The power of a red laser \((\lambda=630 \mathrm{nm})\) is 1.00 watt (abbreviated \(\mathrm{W},\) where \(1 \mathrm{W}=1 \mathrm{J} / \mathrm{s}\) ). How many photons per second does the laser emit?

Starlight The energy density of starlight in interstellar space is \(10^{-15} \mathrm{J} / \mathrm{m}^{3} .\) If the average wavelength of starlight is \(500 \mathrm{nm},\) what is the corresponding density of photons per cubic meter of space?

Why is the Balmer equation considered a special case of the Rydberg equation?

How does the value of \(n\) of an orbit in the Bohr model of hydrogen relate to the energy of an electron in that orbit?

Does the clectromagnetic energy emitted by an excited-state H atom depend on the individual values of \(n_{1}\) and \(n_{2}\) or only on the difference between them \(\left(n_{1}-n_{2}\right) ?\)

Explain the difference between a ground-state \(\mathrm{H}\) atom and an excited-state H atom.

Without calculating any wavelength values, predict which of the following four electron transitions in the hydrogen atom is associated with radiation having the shortest wavelength. a. \(n=1 \rightarrow n=2\) b. \(n=2 \rightarrow n=3\) c. \(n=3 \rightarrow n=4\) d. \(n=4 \rightarrow n=5\)

Without calculating any frequency values, rank the following transitions in the hydrogen atom in order of increasing frequency of the electromagnetic radiation that could produce them. a. \(n=4 \rightarrow n=6\) b. \(n=6 \rightarrow n=8\) c. \(n=9 \rightarrow n=11\) d. \(n=11 \rightarrow n=13\)

Electron transitions from \(n=2\) to \(n=3,4,5,\) or 6 in hydrogen atoms are responsible for some of the Fraunhofer lines in the sun's spectrum. Are there any Fraunhofer lines due to transitions that start from the ground-state hydrogen atoms?

In the visible portion of the atomic emission spectrum of hydrogen, are there any bright lines due to clectron transitions to the ground state?

Balmer observed a hydrogen emission line for the transition from \(n=6\) to \(n=2,\) but not for the transition from \(n=7\) to \(n=2 .\) Why?

In what ways should the cmission spectra of \(\mathrm{H}\) and \(\mathrm{He}^{+}\) be alike, and in what ways should they be different?

What is the wavelength of the photons emitted by hydrogen atoms when they undergo \(n=4 \rightarrow n=3\) transitions? In which region of the electromagnetic spectrum does this radiation occur?

What is the frequency of the photons emitted by hydrogen atoms when they undergo \(n=5 \rightarrow n=3\) transitions? In which region of the electromagnetic spectrum does this radiation occur?

The energies of photons emitted by one-electron atoms and ions fit the equation $$E=\left(2.18 \times 10^{-18} \mathrm{J}\right) \mathrm{Z}^{2}\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right)$$ where \(Z\) is the atomic number, \(n_{1}\) and \(n_{2}\) are positive integers, and \(n_{2}>n_{1} .\) Is the cmission associated with the \(n=2 \rightarrow n=1\) transition in a one-electron ion ever in the visible region? Why or why not?

By absorbing different wavelengths of light, an electron in a hydrogen atom undergoes a transition from \(n=2\) to \(n=3\) and then from \(n=3\) to \(n=4\) a. Are the wavelengths for the two transitions additive that is, does \(\lambda_{2 \rightarrow 4}=\lambda_{2 \rightarrow 3}+\lambda_{3 \rightarrow 4} ?\) b. Are the energies of the two transitions additive-that is, does \(E_{2 \rightarrow 4}=E_{2 \rightarrow 3}+E_{3 \rightarrow 4} ?\)

The hydrogen atomic emission spectrum includes a UV line with a wavelength of \(92.3 \mathrm{nm}\) a. Is this line associated with a transition between different excited states or between an excited state and the ground state? b. What is the energy of the longest-wavelength photon that a ground-state hydrogen atom can absorb?

Identify the symbols in the de Broglie relation, \(\lambda=b / m u\) and explain how the relation links the properties of a particle to those of a wave.

Why do matter waves not add significantly to the challenge of hitting a bascball thrown at 99 mph \((44 \mathrm{m} / \mathrm{s}) ?\)

Would the density or shape of an object have an effect on its de Broglie wavelength?

How does de Broglie's hypothesis that electrons behave like waves explain the stability of the electron orbits in a hydrogen atom?

Two objects are moving at the same speed. Which (if any) of the following statements about them are true? a. The de Broglie wavelength of the heavier object is longer than that of the lighter one. b. If one object has twice as much mass as the other, then its wavelength is one-half the wavelength of the other. c. Doubling the speed of one of the objects will have the same effect on its wavelength as doubling its mass.

Which (if any) of the following statements about the frequency of a particle is true? A Heavy, fast-moving objects have lower frequencies than those of lighter, faster-moving objects. b. Only very light particles can have high frequencies. c. Doubling the mass of an object and halving its speed result in no change in its frequency.

Calculate the wavelengths of the following objects: a. A muon (a subatomic particle with a mass of \(1.884 \times\) \(\left.10^{-28} \mathrm{kg}\right)\) traveling at \(325 \mathrm{m} / \mathrm{s}\) b. Electrons \(\left(m_{c}=9.10938 \times 10^{-31} \mathrm{kg}\right)\) moving at \(4.05 \times\) \(10^{6} \mathrm{m} / \mathrm{s}\) in an electron microscope c. An \(82 \mathrm{kg}\) sprinter running at \(9.9 \mathrm{m} / \mathrm{s}\) d. Earth (mass \(\left.=6.0 \times 10^{24} \mathrm{kg}\right)\) moving through space at \(3.0 \times 10^{4} \mathrm{m} / \mathrm{s}\)

How rapidly would each of the following particles be moving if they all had the same wavelength as a photon of red light \((\lambda=750 \mathrm{nm}) ?\) a. An electron of mass \(9.10938 \times 10^{-28} \mathrm{g}\) b. A proton of mass \(1.67262 \times 10^{-24} \mathrm{g}\) c. A neutron of mass \(1.67493 \times 10^{-24} \mathrm{g}\) d. An \(\alpha\) particle of mass \(6.64 \times 10^{-24} \mathrm{g}\)

How does the concept of an orbit in the Bohr model of the hydrogen atom differ from the concept of an orbital in quantum theory?