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 97P: For an electron in a hydrogen atom in the n=2 state, compute: (a) the angular momentum; (b) the...
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Concept explainers
An electron in hydrogen is in the 5ff state.
A) Find the largest possible value of the z component of its angular momentum .
Express your answer in terms of ℏℏ.
B) For the electron in part A, find the value of the expression L2x+L2y−−−−−−−√Lx2+Ly2.
Express your answer in terms of ℏℏhbar.
Definition Definition Product of the moment of inertia and angular velocity of the rotating body: (L) = Iω Angular momentum is a vector quantity, and it has both magnitude and direction. The magnitude of angular momentum is represented by the length of the vector, and the direction is the same as the direction of angular velocity.
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