Chapter 7

Use representations \([\mathrm{A}]\) through \([\mathrm{I}]\) in Figure \(\mathrm{P} 7.10\) to answer questions a-f. a. Compare [A] and [H]. Which valence electron experiences the larger \(Z_{\text {cff }} ?\) Which is more shielded from the positive charge of the nucleus? Which has the lower \(\mathrm{IE}_{1} ?\) b. Which representation depicts the loss of an electron? c. Which representations can be discussed using only a quantized model of light? d. Which representations are consistent with the model of an atom that discusses probability with regard to the location of electrons? e. What do the arrows represent in \([\mathrm{E}]\) and \([\mathrm{I}] ?\) f. Which representation conveys that the probability of finding an electron at the nucleus is zero?

Describe the similarities and differences between the atomic emission and absorption spectra of hydrogen.

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

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

What would happen to the appearance of the Fraunhofer lines in the solar spectrum if sunlight were passed through a flame containing high-temperature calcium atoms and then analyzed?

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

Ultraviolet radiation causes skin damage that may lead to cancer, but exposure to infrared radiation does not seem to cause skin cancer. Why do you think this is so?

Gamma rays are an example of "ionizing" radiation because they have the energy to break apart molecules into molecular ions and free electrons. What other forms of electromagnetic radiation could also be ionizing radiation?

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

In each pair, which radiation has higher frequency? (a) ultraviolet or infrared radiation; (b) visible light or gamma rays; (c) microwaves or radio waves

In each pair, which radiation has longer wavelength? (a) visible light or microwaves; (b) radio waves or gamma rays; (c) infrared or ultraviolet radiation

If the wavelength of a photon of red light is twice that of a photon of ultraviolet radiation, how much more energy does the UV photon have?

If the frequency of a photon of red light is twice that of a photon of infrared radiation, how much more energy does the photon of red light have?

A neon light emits radiation of \(\lambda=616 \mathrm{nm} .\) What is the frequency of this radiation?

In the 1990 s 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 \(82 \mathrm{Hz}\), whereas 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?

FM radio stations broadcast at different frequencies. Calculate the wavelengths corresponding to the broadcast frequencies of the following college radio stations: (a) KCSU-FM (Fort Collins, CO), \(90.5 \mathrm{MHz} ;\) (b) WVUD (Newark, DE), \(91.3 \mathrm{MHz} ;\) (c) KUCR (Riverside, CA), \(88.3 \mathrm{MHz}\)

Which radiation has the longer wavelength: (a) radio waves from an AM radio station broadcasting at \(680 \mathrm{kHz}\) or (b) infrared radiation emitted by the surface of Earth \((\lambda=15 \mu \mathrm{m}) ?\)

Which radiation has the lower frequency: (a) radio waves from an AM radio station broadcasting at \(1030 \mathrm{kHz}\) or (b) the red light \((\lambda=633 \mathrm{nm})\) from a helium-neon laser?

Which radiation has the higher frequency: (a) the red light on a bar-code reader at a grocery store or (b) the green light on the battery charger for a laptop computer?

How long does it take moonlight to reach Earth when the distance to the moon is \(384,000 \mathrm{km} ?\)

What is the difference between a quantum and a photon?

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

What effect does the intensity (amplitude) of a wave have on the emission of electrons from a surface, if we assume that the frequency of incident radiation is above the threshold frequency?

Has a photon of radiation that is shifted to a longer wavelength by \(10 \%\) actually lost \(10 \%\) of its energy?

Which of the following have quantized values? 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 speed 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

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 electrons with the longer wavelength? What is the wavelength of the electrons emitted by the titanium surface?

Solar Power Photovoltaic cells convert solar energy into electricity. Could tantalum \(\left(\phi=6.81 \times 10^{-19} \mathrm{J}\right)\) be used to convert visible light to electricity? Assume that most of the electromagnetic energy from the Sun is in the visible region near \(500 \mathrm{nm}\)

With reference to Problem \(7.41,\) could tungsten \((\phi=7.20 \times\) \(\left.10^{-19} \mathrm{J}\right)\) be used to construct solar cells?

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?

Why should hydrogen have the simplest atomic spectrum of all the elements?

For an electron in a hydrogen atom, how is the value of \(n\) of its orbit related to its energy?

Does the electromagnetic 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 \(\mathrm{H}\) atom.

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

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. from \(n=4\) to \(n=6\) b. from \(n=6\) to \(n=8\) c. from \(n=9\) to \(n=11\) d. from \(n=11\) to \(n=13\)

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 \(n=3\) in hydrogen atoms?

In the visible portion of the atomic emission spectrum of hydrogen, are there any bright lines due to electron transitions to the \(n=1\) 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 emission 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 transitions from \(n=4\) to \(n=3 ?\) 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 transitions from \(n=5\) to \(n=3 ?\) In which region of the electromagnetic spectrum does this radiation occur?

The energies of the photons emitted by one-electron atoms and ions fit the equation $$E=\left(2.178 \times 10^{-18} \mathrm{J}\right) \mathrm{Z}^{2}\left(\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right)$$ where \(Z\) is the atomic number, \(n_{2}\) and \(n_{1}\) are positive integers, and \(n_{2}>n_{1}\) a. As the value of \(Z\) increases, does the wavelength of the photon associated with the transition from \(n=2\) to \(n=1\) increase or decrease? b. Can the wavelength associated with the transition from \(n=2\) to \(n=1\) ever be observed in the visible region of the spectrum?

Can transitions from higher energy states to the \(n=2\) level in He \(^{+}\) ever produce visible light? If so, for what values of \(n_{2} ?\) (Hint: The equation in Problem 7.57 may be useful.)

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 value of \(n_{1}\) of this transition? c. 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.

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

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

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

Calculate the wavelengths of the following objects: a. a muon (a subatomic particle with a mass of \(1.884 \times\) \(\left.10^{-25} \mathrm{g}\right)\) traveling at \(325 \mathrm{m} / \mathrm{s}\) b. electrons \(\left(m_{c}=9.10938 \times 10^{-28} \mathrm{g}\right)\) moving at \(4.05 \times\) \(10^{6} \mathrm{m} / \mathrm{s}\) in an electron microscope c. an \(80-\mathrm{kg}\) athlete running a 4 -minute mile d. Earth (mass \(=6.0 \times 10^{27} \mathrm{g}\) ) moving through space at \(3.0 \times 10^{4} \mathrm{m} / \mathrm{s}\)