29.1 Quantization of Energy
The visible spectrum of sunlight shows a range of colors from red to violet. This spectrum has numerous dark lines spread throughout it. Noting that the surface of the Sun is much cooler than the interior, so that the surface is comparable to a cool gas through which light passes, which of the following statements correctly explains the dark lines?
- The cooler, denser surface material scatters certain wavelengths of light, forming dark lines.
- The atoms at the surface absorb certain wavelengths of light, causing the dark lines at those wavelengths.
- The atoms in the Sun’s interior emit light of specific wavelength, so that parts of the spectrum are dark.
- The atoms at the surface are excited by the high interior temperatures, so that the dark lines are merely wavelengths at which those atoms don’t emit energy.
A log in a fireplace burns for nearly an hour, at which point it consists mostly of small, hot embers. These embers glow a bright orange and whitish-yellow color. Describe the characteristics of the energy of this system, both in terms of energy transfer and the quantum behavior of blackbodies.
29.2 The Photoelectric Effect
A metal exposed to a beam of light with a wavelength equal to or shorter than a specific wavelength emits electrons. What property of light, as described in the quantum explanation of blackbody radiation, accounts for this photoelectric process?
- The energy of light increases as its speed increases.
- The energy of light increases as its intensity increases.
- The energy of light increases as its frequency increases.
- The energy of light increases as its wavelength increases.
During his experiments that confirmed the existence of electromagnetic waves, Heinrich Hertz used a spark across a gap between two electrodes to provide the rapidly changing electric current that produced electromagnetic waves. He noticed, however, that production of the spark required a lower voltage in a well-lighted laboratory than when the room was dark. Describe how this curious event can be explained in terms of the quantum interpretation of the photoelectric effect.
29.3 Photon Energies and the Electromagnetic Spectrum
A microwave oven produces electromagnetic radiation in the radio portion of the spectrum. These microwave photons are absorbed by water molecules, resulting in an increase in the molecules’ rotational energies. This added energy is transferred by heat to the surrounding food, which as a result becomes hot very quickly. If the energy absorbed by a water molecule is 1.0 × 10–5 eV, what is the corresponding wavelength of the microwave photons?
- 1.22 GHz
- 2.45 GHz
- 4.90 GHz
- 9.80 Hz
In the intensity versus frequency curve for x rays (Figure 29.14), the intensity is mostly a smooth curve associated with bremsstrahlung (“breaking radiation”). However, there are two spikes (characteristic x rays) that exhibit high-intensity output. Explain how the smooth curve can be described by classical electrodynamics, whereas the peaks require a quantum mechanical interpretation. (Recall that the acceleration or deceleration of electric charges causes the emission of electromagnetic radiation.)
29.4 Photon Momentum
The mass of a proton is 1.67 × 10–27 kg. If a proton has the same momentum as a photon with a wavelength of 325 nm, what is its speed?
- 2.73 × 10–3 m/s
- 0.819 m/s
- 1.22 m/s
- 2.71 × 104 m/s
A strip of metal foil with a mass of 5.00 × 10–7 kg is suspended in a vacuum and exposed to a pulse of light. The velocity of the foil changes from zero to 1.00 × 10–3 m/s in the same direction as the initial light pulse, and the light pulse is entirely reflected from the surface of the foil. Given that the wavelength of the light is 450 nm, and assuming that this wavelength is the same before and after the collision, how many photons in the pulse collide with the foil?
29.4 Photon Momentum
In an experiment in which the Compton effect is observed, a “gamma ray” photon with a wavelength of 5.00 × 10–13 m scatters from an electron. If the change in the electron energy is 1.60 × 10–15 J, what is the wavelength of the photon after the collision with the electron?
- 4.95 × 10–13 m
- 4.98 × 10–13 m
- 5.02 × 10–13 m
- 5.05 × 10–13 m
Consider two experiments involving a metal sphere with a radius of 2.00 μm that is suspended in a vacuum. In one experiment, a pulse of N photons reflects from the surface of the sphere, causing the sphere to acquire momentum. In a second experiment, an identical pulse of photons is completely absorbed by the sphere, so that the sphere acquires momentum. Identify each type of collision as either elastic or inelastic, and, assuming that the change in the photon wavelength can be ignored, use linear momentum conservation to derive the expression for the momentum of the sphere in each experiment.
29.5 The Particle-Wave Duality
The ground state of a certain type of atom has energy of –E0. What is the wavelength of a photon with enough energy to ionize the atom when it is in the ground state, so that the ejected electron has kinetic energy equal to 2E0?
While the quantum model explains many physical processes that the classical model cannot, it must be consistent with those processes that the classical model does explain. Energy and momentum conservation are fundamental principles of classical physics. Use the Compton and photoelectric effects to explain how these conservation principles carry over to the quantum model of light.
29.6 The Wave Nature of Matter
The least massive particle known to exist is the electron neutrino. Though scientists once believed that it had no mass, like the photon, they have now determined that this particle has an extremely low mass, equivalent to a few electron volts. Assuming a mass of 2.2 eV/c2 (or 3.9 × 10–36 kg) and a speed of 4.4 × 106 m/s, which of the following values equals the neutrino’s de Broglie wavelength?
- 3.8 × 10–5 m
- 4.7 × 10–7 m
- 1.7 × 10–10 m
- 8.9 × 10–14 m
Using the definition of the de Broglie wavelength, explain how wavelike properties of matter increase with a decrease in mass or decrease in speed. Use as examples an electron (mass = 9.11 × 10–31 kg) with a speed of 5.0 × 106 m/s and a proton (mass = 1.67 × 10–27 kg) with a speed of 8.0 × 106 m/s.
29.6 The Wave Nature of Matter
In a Davisson-Germer type of experiment, a crystal with a parallel-plane separation (d) of 9.1 × 10–2 nm produces constructive interference with an electron beam at an angle of θ = 50°. Which of the following is the maximum de Broglie wavelength for these electrons?
- 0.09 nm
- 0.14 nm
- 0.21 nm
In a Davisson-Germer experiment, electrons with a speed of 6.5 × 106 m/s exhibit third-order (n = 3) constructive interference for a crystal with unknown plane separation, d. Given an angle of incidence of θ = 45°, compute the value for d. Compare the de Broglie wavelength to electromagnetic radiation with the same wavelength. (Recall that the mass of the electron is 9.11 × 10–31 kg.)
29.8 The Particle-Wave Duality Reviewed
Which of the following describes one of the main features of wave-particle duality?
- As speed increases, the wave nature of matter becomes more evident.
- As momentum decreases, the particle nature of matter becomes more evident.
- As energy increases, the wave nature of matter becomes easier to observe.
- As mass increases, the wave nature of matter is less easy to observe.
Explain why Heisenberg’s uncertainty principle limits the precision with which either momentum or position of a subatomic particle can be known, but becomes less applicable for matter at the macroscopic level.