1 The Nature Of Light 2 Geometric Optics And Image Formation 3 Interference 4 Diffraction 5 Relativity 6 Photons And Matter Waves 7 Quantum Mechanics 8 Atomic Structure 9 Condensed Matter Physics 10 Nuclear Physics 11 Particle Physics And Cosmology Chapter6: Photons And Matter Waves
Chapter Questions Section: Chapter Questions
Problem 6.1CYU: Check Your Understanding The flame of a peach-scented candle has a yellowish color and the flame of... Problem 6.2CYU: Check Your Understanding An iron poker is being heated. As its temperature rises, the poker begins... Problem 6.3CYU: Check Your Understanding Suppose that two stars, and . radiate exactly the same total power. If... Problem 6.4CYU: Check Your Understanding A molecule is vibrating at a frequency of 5.010Hz. What is the smallest... Problem 6.5CYU: Check Your Understanding Would the result in Example 6.4 be different if the mass were not 1.0 kg g... Problem 6.6CYU: Check Your Understanding A yellow 589-nm light is incident on a surface whose work function is 1.20... Problem 6.7CYU: Check Your Understanding Cut-off frequency for the photoelectric effect in some materials is 8.01013... Problem 6.8CYU: Check Your Understanding An incident 71-pm X-ray is incident on a calcite target. Find the... Problem 6.9CYU: Check Your Understanding What are the limits of the Lyman series? Can you see these spectral lines? Problem 6.10CYU: Check Your Understanding When an election in a hydrogen atom is in the first excited state, what... Problem 6.11CYU: Check Your Understanding What is de Broglie’s wavelength of a non-relativistic proton with a kinetic... Problem 6.12CYU: Check Your Understanding Find the de Broglie wavelength of an electron in the third excited state of... Problem 6.13CYU: Check Your Understanding Find the de Brogue wavelength and kinetic energy of a free electron that... Problem 6.14CYU: Check Your Understanding For the situation described in Example 6.15, find the angular position of... Problem 6.15CYU: Check Your Understanding Suppose that the diameter of the aperture in Example 6.16 is halved. How... Problem 1CQ: Which surface has a higher temperature — the surface of a yellow star or that of a red star? Problem 2CQ: Describe what you would see when looking at a body whose temperature is increased from 1000 K to... Problem 3CQ: Explain the color changes in a hot body as its temperature is increased. Problem 4CQ: Speculate as to why UV light causes sunburn, whereas visible light does not. Problem 5CQ: Two cavity radiators are constructed with walls made of different metals. At the same temperature,... Problem 6CQ: Discuss why some bodies appear black, other bodies appear red, and still other bodies appear white. Problem 7CQ: If everything radiates electromagnetic energy, why can we not see objects at room temperature in a... Problem 8CQ: How much does the power radiated by a blackbody increase when its temperature (in K) is tripled? Problem 9CQ: For the same monochromatic light source, would the photoelectric effect occur for all metals? Problem 10CQ: In the interpretation of the photoelectric effect, how is it known that an electron does not absorb... Problem 11CQ: Explain how you can determine the work function from a plot of the stopping potential versus the... Problem 12CQ: Suppose that in the photoelectric-effect experiment we make a plot of the detected current versus... Problem 13CQ: Speculate how increasing the temperature of a photoelectrode affects the outcomes of the... Problem 14CQ: Which aspects of the photoelectric effect cannot be explained by classical physics? Problem 15CQ: Is the photoelectric effect a consequence of the wave character of radiation or is it a consequence... Problem 16CQ: The metals sodium, iron, and molybdenum have work functions 25 eV, 3.9 eV, and 4.2 eV, respectively.... Problem 17CQ: Discuss any similarities and differences between the photoelectric and the Compton effects. Problem 18CQ: Which has a greater momentum: an UV photon or an IR photon? Problem 19CQ: Does changing the intensity of a monochromatic light beam affect the momentum of the individual... Problem 20CQ: Can the Compton effect occur with visible light? If so, will it be detectable? Problem 21CQ: Is it possible in the Compton experiment to observe scattered X-rays that have a shorter wavelength... Problem 22CQ: Show that the Compton wavelength has the dimension of length. Problem 23CQ: At what scattering angle is the wavelength shift in the Compton effect equal to the Compton... Problem 24CQ: Explain why the patterns of bright emission spectral lines have an identical spectral position to... Problem 25CQ: Do the various spectral lines of the hydrogen atom overlap? Problem 26CQ: The Balmer series for hydrogen was discovered before either the Lyman or the Paschen series. Why? Problem 27CQ: When the absorption spectrum of hydrogen at room temperature is analyzed, absorption lines for the... Problem 28CQ: Hydrogen accounts for about 75% by mass of the matter at the surfaces of most stars. However, the... Problem 29CQ: Discuss the similarities and differences between Thomson’s model of the hydrogen atom and Bohr’s... Problem 30CQ: Discuss the way in which Thomson’s model is nonphysical. Support your argument with experimental... Problem 31CQ: If, in a hydrogen atom, an electron moves to an orbit with a larger radius, does the energy of the... Problem 32CQ: How is the energy conserved when an atom makes a transition from a higher to a lower energy state? Problem 33CQ: Suppose an electron in a hydrogen atom makes a transition from the (n+1) th orbit to the nth orbit.... Problem 34CQ: Discuss why the allowed energies of the hydrogen atom are negative. Problem 35CQ: Can a hydrogen atom absorb a photon whose energy is greater than 13.6 eV? Problem 36CQ: Why can you see through glass but not through wood? Problem 37CQ: Do gravitational forces have a significant effect on atomic energy levels? Problem 38CQ: Show that Planck’s constant has the dimensions of angular momentum. Problem 39CQ: Which type of radiation is most suitable for the observation of diffraction patterns on crystalline... Problem 40CQ: Speculate as to how the diffraction patterns of a typical crystal would be affected if -rays were... Problem 41CQ: If an electron and a proton are traveling at the same speed, which one has the shorter de Brogue... Problem 42CQ: If a particle is accelerating, how does this affect its de Brogue wavelength? Problem 43CQ: Why is the wave-like nature of matter not observed every day for macroscopic objects? Problem 44CQ: What is the wavelength of a neutron at rest? Explain. Problem 45CQ: Why does the setup of Davisson—Germer experiment need to be enclosed in a vacuum chamber? Discuss... Problem 46CQ: Give an example of an experiment in which light behaves as waves. Give an example of an experiment... Problem 47CQ: Discuss: How does the interference of water waves differ from the interference of electrons? How are... Problem 48CQ: Give at least one argument in support of the matter-wave hypothesis. Problem 49CQ: Give at least one argument in support of the particle-nature of radiation. Problem 50CQ: Explain the importance of the Young double-slit experiment. Problem 51CQ: Does the Heisenberg uncertainty principle allow a particle to be at rest in a designated region in... Problem 52CQ: Can the de Brogue wavelength of a particle be known exactly? Problem 53CQ: Do the photons of red light produce better resolution in a microscope than blue light photons?... Problem 54CQ: Discuss the main difference between an SEM and a TEM. Problem 55P: A 200-W heater emits a 1.5-m radiation. (a) What value of the energy quantum does it emit? (b)... Problem 56P: A 900-W microwave generator in an oven generates energy quanta of frequency 2560 MHz. (a) How many... Problem 57P: (a) For what temperature is the peak of blackbody radiation spectrum at 400 nm? (b) If the... Problem 58P: The tungsten elements of incandescent light bulbs operate at 3200 K. At what frequency does the... Problem 59P: Interstellar space is filled with radiation of wavelength 970µn. This radiation is considered to be... Problem 60P: The radiant energy from the sun reaches its maximum at a wavelength of about 500.0 nm. What is the... Problem 61P: A photon has energy 20 keV. What are its frequency and wavelength? Problem 62P: The wavelengths of visible light range from approximately 400 to 750 nm. What is the corresponding... Problem 63P: What is the longest wavelength of radiation that can eject a photoelectron from silver? Is it in the... Problem 64P: What is the longest wavelength of radiation that can eject a hotoelectron from potassium, given the... Problem 65P: Estimate the binding energy of electrons in magnesium, given that the wavelength of 337 nm is the... Problem 66P: The work function for potassium is 2.26 eV. What is the cutoff frequency when this metal is used as... Problem 67P: Estimate the work function of aluminum, given that the wavelength of 304 nm is the longest... Problem 68P: What is the maximum kinetic energy of photoelectrons ejected from sodium by the incident radiation... Problem 69P: A 120-nm UV radiation illuminates a gold-plated electrode. What is the maximum kinetic energy of the... Problem 70P: A 400-nm violet light ejects photoelectrons with a maximum kinetic energy of 0.860 eV from sodium... Problem 71P: A 600-nm light falls on a photoelectric surface and electrons with the maximum kinetic energy of... Problem 72P: The cutoff wavelength for the emission of photoelectrons from a particular surface is 500 nm. Find... Problem 73P: Find the wavelength of radiation that can eject 2.00-eV electrons from calcium electrode. The work... Problem 74P: Find the wavelength of radiation that can eject 0.10-eV electrons from potassium electrode. The work... Problem 75P: Find the maximum velocity of photoelectrons ejected by an 80-nm radiation, if the work function of... Problem 76P: What is the momentum of a 589-nm yellow photon? Problem 77P: What is the momentum of a 4-cm microwave photon? Problem 78P: In a beam of white light (wavelengths from 400 to 750 nm), what range of momentum can the photons... Problem 79P: What is the energy of a photon whose momentum is 3.01024 kg• m/s ? Problem 80P: What is the wavelength of (a) a 12-keV X-ray photon; (b) a 2.O-MeV y -ray photon? Problem 81P: Find the momentum and energy of a 1.0-Å photon. Problem 82P: Find the wavelength and energy of a photon with momentum 5.001029 kg•m/s. Problem 83P: A -ray photon has a momentum of 8.001021 kg • m/s. Find its wavelength and energy. Problem 84P: (a) Calculate the momentum of a 2.5-pm photon. (b) Find the velocity of an electron with the same... Problem 85P: Show that p=h and Ef=hf are consistent with the relativistic formula E2=p2c2+m02c2 . Problem 86P: Show that the energy E in eV of a photon is given by E=1.241106 m/A. where A is its wavelength in... Problem 87P: For collisions with free electrons, compare the Compton shift of a photon scattered as an angle of... Problem 88P: X-rays of wavelength 12.3 pm are scattered from a block of carbon. What are the wavelengths of... Problem 89P: Calculate the wavelength of the first line in the Lyman series and show that this line lies in the... Problem 90P: Calculate the wavelength of the fifth line in the Lyman series and show that this line lies in the... Problem 91P: Calculate the energy changes corresponding to the transitions of the hydrogen atom: (a) from n=3 to... Problem 92P: Determine the wavelength of the third Balmer line (transition from n=5 to n=2 ). Problem 93P: What is the frequency of the photon absorbed when the hydrogen atom makes the transition from the... Problem 94P: When a hydrogen atom is in its ground state, what are the shortest and longest wavelengths of the... Problem 95P: When a hydrogen atom is in its third excided state, what are the shortest and longest wavelengths of... Problem 96P: What is the longest wavelength that light can have if it is to be capable of ionizing the hydrogen... Problem 97P: For an electron in a hydrogen atom in the n=2 state, compute: (a) the angular momentum; (b) the... Problem 98P: Find the ionization energy of a hydrogen atom in the fourth energy state. Problem 99P: It has been measured that it required 0.850 eV to remove an electron from the hydrogen atom. In what... Problem 100P: What is the radius of a hydrogen atom when the electron is in the first excited state? Problem 101P: Find the shortest wavelength in the Balmer series. In what part of the spectrum does this line lie? Problem 102P: Show that the entire Paschen series lies in the infrared part of the spectrum. Problem 103P: Do the Balmer series and the Lyman series overlap? Why? Why not? (Hint: calculate the shortest... Problem 104P: (a) Which line in the Balmer series is the first one in the UV part of the spectrum? (b) How many... Problem 105P: A 4.653-urn emission line of atomic hydrogen corresponds to transition between the states nf=5 and... Problem 106P: At what velocity will an electron have a wavelength of 1.00 m? Problem 107P: What is the de Brogue wavelength of an electron travelling at a speed of 5.0106 m/s ? Problem 108P: What is the de Brogue wavelength of an electron that is accelerated from rest through a potential... Problem 109P: What is the de Brogue wavelength of a proton whose kinetic energy is 2.0 MeV? 10.0 MeV? Problem 110P: What is the de Brogue wavelength of a 10-kg football player running at a speed of 8.0 m/s? Problem 111P: (a) What is the energy of an electron whose de Brogue wavelength is that of a photon of yellow light... Problem 112P: The de Brogue wavelength of a neutron is 0.01 nm. What is the speed and energy of this neutron? Problem 113P: What is the wavelength of an electron that is moving at a 3% of the speed of light? Problem 114P: At what velocity does a proton have a 6.0-fm wavelength (about the size of a nucleus)? Give your... Problem 115P: What is the velocity of a 0.400-kg billiard ball if its wavelength is 7.50 fm? Problem 116P: Find the wavelength of a proton that is moving at 1.00% of the speed of light (when =0.01). Problem 117P: An AM radio transmitter radiates 500 kW at a frequency of 760 kHz. How many photons per second does... Problem 118P: Find the Lorentz factor and de Brogue’s wavelength for a 50-GeV electron in a particle accelerator. Problem 119P: Find the Lorentz factor and de Brogue’s wavelength for a 1.O-TeV proton in a particle accelerator. Problem 120P: What is the kinetic energy of a 0.01-nm electron in a TEM? Problem 121P: If electron is to be diffracted significantly by a crystal, its wavelength must be about equal to... Problem 122P: X-rays form ionizing radiation that is dangerous to living tissue and undetectable to the human eye.... Problem 123P: Solar wind (radiation) that is incident on the top of Earth’s atmosphere has an average intensity of... Problem 124P: Treat the human body as a blackbody and determine the percentage increase in the total power of its... Problem 125P: Show that Wien’s displacement law results from Planck’s radiation law. (Him: substitute x=hckT and... Problem 126P: Show that Stefan’s law results from Planck’s radiation law. Hin: To compute the total power of... Problem 127AP: Determine the power intensity of radiation per unit wavelength emitted at a wavelength of 500.0 nm... Problem 128AP: The HC1 molecule oscillates at a frequency of 87.0 THz. What is the difference (in eV) between its... Problem 129AP: A quantum mechanical oscillator vibrates at a frequency of 250.0 THz. What is the minimum energy of... Problem 130AP: In about 5 billion years, the sun will evolve to a red giant. Assume that its surface temperature... Problem 131AP: A sodium lamp emits 2.0 W of radiant energy, most of which has a wavelength of about 589 nm.... Problem 132AP: Photoelectrons are ejected from a photo electrode and are detected at a distance of 2.50 cm away... Problem 133AP: If the work function of a metal is 3.2 eV, what is the maximum wavelength that a photon can have to... Problem 134AP: The work function of a photoelectric surface is 2.00 eV. What is the maximum speed of the... Problem 135AP: A 400-nm laser beam is projected onto a calcium electrode. The power of the laser beam is 2.00 mW... Problem 136AP: (a) Calculate the number of photoelectrons per second that are ejected from a 1.00-mm2 area of... Problem 137AP: A laser with a power output of 2.00 mW at a 400-nm wavelength is used to project a beam of light... Problem 138AP: The work function for barium is 2.48 eV. Find the maximum kinetic energy of the ejected... Problem 139AP: (a) Calculate the wavelength of a photon that has the same momentum as a proton moving with 1% of... Problem 140AP: (a) Find the momentum of a 100-keV X-ray photon. (b) Find the velocity of a neutron with the same... Problem 141AP: The momentum of light, as it is for particles, is exactly reversed when a photon is reflected... Problem 142AP: A photon of energy 5.0 keV collides with a stationary electron and is scattered at an angle of 60°.... Problem 143AP: A 0.75-nm photon is scattered by a stationary electron. The speed of the electron’s recoil is 1.5106... Problem 144AP: Find the maximum change in X-ray wavelength that can occur due to Compton scattering. Does this... Problem 145AP: A photon of wavelength 700 nm is incident on a hydrogen atom. When this photon is absorbed, the atom... Problem 146AP: What is the maximum kinetic energy of an electron such that a collision between the electron and a... Problem 147AP: Singly ionized atomic helium He +1 is a hydrogen-like ion. (a) What is its ground-state radius? (b)... Problem 148AP: A triply ionized atom of betyllium Be3+ is a hydrogen-like ion. When Be3+ is in one of its excited... Problem 149AP: In extreme-temperature environments, such as those existing in a solar corona, atoms may be ionized... Problem 150AP: (a) Calculate the ionization energy for He+. (b) What is the minimum frequency of a photon capable... Problem 151AP: Experiments are performed with ultracold neutrons having velocities as small as 1.00 m/s. Find the... Problem 152AP: Find the velocity and kinetic energy of a 6.0-fm neutron. (Rest mass energy of neutron is E0=940... Problem 153AP: The spacing between crystalline planes in the NaC1 crystal is 0.281 nm, as determined by X-ray... Problem 154AP: What is the wavelength of an electron accelerated from rest in a 30.0-kV potential difference? Problem 155AP: Calculate the velocity of a 1.0-m electron and a potential difference used to accelerate it from... Problem 156AP: In a supercollider at CERN, protons are accelerated to velocities of 0.25c. What are their... Problem 157AP: Find the de Brogue wavelength of an electron accelerated from rest in an X-ray rube in the potential... Problem 158AP: The cutoff wavelength for the emission of photoelectrons from a particular surface is 500 nm. Find... Problem 159AP: Compare the wavelength shift of a photon scattered by a free electron to that of a photon scattered... Problem 160AP: The spectrometer used to measure the wavelengths of the scattered X-rays in the Compton experiment... Problem 161AP: Consider a hydrogen-like ion where an electron is orbiting a nucleus that has charge q=+Ze. Derive... Problem 162AP: Assume that a hydrogen atom exists in the n=2 excited state for 108 s before decaying to the ground... Problem 163AP: An atom can be formed when a negative muon is captured by a proton. The muon has the same charge as... Problem 11CQ: Explain how you can determine the work function from a plot of the stopping potential versus the...
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Concept explainers
Circle TRUE or FALSE for each of the following statements about the photoelectric effect . Justify each answer in 1–2 sentences:
The stopping potential for the photoelectrons is zero at the cutoff wavelength for the incident photons: TRUE / FALSE
The intensity of the incident light has no effect on the photoelectric effect: TRUE / FALSE
Definition Definition Phenomenon in which a substance absorbs electromagnetic radiation and electrically charged particles are emitted from or inside it.
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