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physics
modern physics

University Physics With Modern Physics 2nd edition Wolfgang Bauer, Gary Westfall - Solutions

White light (400. nm < λ < 700. nm) shines onto a puddle of water (n = 1.33). There is a thin (100.0 nm thick) layer of oil (n = 1.47) on top of the water. What wavelengths of light would you see reflected?
Some mirrors for infrared lasers are constructed with alternating layers of hafnia and silica. Suppose you want to produce constructive interference from a thin film of hafnia (n = 1.90) on BK-7 glass (n = 1.51) using infrared radiation of wavelength 1.06 μ,m. What is the smallest film thickness
Sometimes thin films are used as filters to prevent certain colors from entering a lens. Suppose an infrared filter is to be designed to prevent 800.0-nm light from entering a lens. Find the minimum thickness for a film of MgF2 (n = 1.38) that will prevent this light from entering the lens.
White light shines on a sheet of mica that has a uniform thickness of 1.30 μ.m. When the reflected light is viewed using a spectrometer, it is noted that light with wavelengths of 433.3 nm, 487.5 nm, 557.1 nm, 650.0 nm, and 780.0 nm is not present in the reflected light. What is the index of
A single beam of coherent light (Î» = 633 ˆ™ 10-9 m) is incident on two glass slides, which are touching at one end and are separated by a 0.0200-mm-thick sheet of paper on the other end, as shown in the figure. Beam 1 reflects off the bottom surface of the top slide, and beam 2 reflects off
A common interference setup for seeing Newton's rings consists of a plano-convex lens placed on a plane mirror and illuminated from above at normal incidence with monochromatic light. In an experiment using a plano-convex lens with local length f = 80.00 cm and index of refraction n1 = 1.500, the
A Michelson interferometer is used in a class of commercially available optical instruments called wavelength meters. In a wavelength meter, the interferometer is illuminated simultaneously with parallel beams from a reference laser of known wavelength and an unknown laser. The movable mirror of
At the Long-baseline Interferometer Gravitational-wave Observatory (LIGO) facilities in Hanford, Washington, and Livingston, Louisiana, laser beams of wavelength 550.0 nm travel along perpendicular paths 4.000 km long. Each beam is reflected along its path and back 100 times before the beams are
Light of wavelength 653 nm illuminates a single slit. If the angle between the first dark fringes on either side of the central maximum is 32.0°, what is the width of the slit?
An instructor uses light of wavelength 633 nm to create a diffraction pattern with a slit of width 0.135 mm. How far away from the slit must the instructor place the screen in order for the full width of the central maximum to be 5.00 cm?
What is the largest slit width for which there are no minima when the wavelength of the incident light on the single slit is 600.nm?
Plane microwaves are incident on a single slit of width 2.00 cm. The second minimum is observed at an angle of 43.0°. What is the wavelength of the microwaves?
The Large Binocular Telescope (LBT), on Mount Graham near Tucson, Arizona, has two 8.4-m-diameter primary mirrors. The mirrors are centered a distance of 14.4 m apart, thus producing a mirror with an effective diameter of 14.4 m. What is the minimum angular resolution of the LBT for green light (A
A canvas tent has a single, tiny hole in its side. On the opposite wall of the tent, 2.0 m away, you observe a dot (due to sunlight incident upon the hole) of width 2.0 mm, with a faint ring around it. What is the size of the hole in the tent? (Assume a wave length of 570 nm for the sunlight.)
In mechanics, one often uses the model of a perfectly rigid body to determine the motion of physical objects (see, for example. Chapter 10 on rotation). Explain how this model contradicts Einstein's special theory of relativity.
Use light cones and world lines to help solve the following problem. Eddie and Martin are throwing water balloons very fast at a target. At t = - 13 μ,s, the target is at x = 0, Eddie is at x = -2 km, and Martin is at x = 5 km; all three remain in these positions for all time. The target is hit at
A gravitational lens should produce a halo effect and not arcs. Given that the light travels not only to the right and left of the intervening massive object but also to the top and bottom, why do we typically see only arcs?
Suppose you are explaining the theory of relativity to a friend, and you tell him that nothing can go faster than 300,000 km/s. He says that is obviously false: Suppose a spaceship traveling past you at 200,000 km/s, which is perfectly possible according to what you are saying, fires a torpedo
Consider a positively charged particle moving at constant speed parallel to a current-carrying wire, in the direction of the current. As you know (after studying Chapters 27 and 28), the particle is attracted to the wire by the magnetic force due to the current. Now suppose another observer moves
At rest, a rocket has an overall length of L. A garage at rest (built for the rocket by the lowest bidder) is only L/2 in length. Luckily, the garage has both a front door and a back door, so that when the rocket flies at a speed of v = 0.866c, it fits entirely into the garage. However, according
A rod at rest on Earth makes an angle of 10° with the x-axis. If the rod is moved along the x-axis, what happens to this angle, as viewed by an observer on the ground?
An astronaut in a spaceship flying toward Earth's Equator at half the speed of light observes Earth to be an oblong solid, wider and taller than it appears deep, rotating around its long axis. A second astronaut flying toward Earth's North Pole at half the speed of light observes Earth to be a
Consider two clocks carried by observers in a reference frame moving at speed v in the positive x-direction relative to Earth's rest frame. Assume that the two reference frames have parallel axes and that their origins coincide when clocks at that point in both frames read zero. Suppose the clocks
Prove that in all cases, adding two sub-light-speed velocities relativistically will always yield a sub-light-speed velocity. Consider motion in one spatial dimension only.
A famous result in Newtonian dynamics is that if a particle in motion collides elastically with an identical particle at rest, the two particles emerge from the collision on perpendicular trajectories. Does the same hold in the special theory of relativity? Suppose a particle of rest mass m and
Suppose you are watching a spaceship orbiting Earth at 80% of the speed of light. What is the length of the ship as viewed from the center of the orbit?
Find the speed of light in feet per nanosecond, to three significant figures.
Find the value of g, the gravitational acceleration at Earth's surface, in light-years per year per year, to three significant figures.
Michelson and Morley used an interferometer to show that the speed of light is constant, regardless of Earth's motion through any purported luminiferous aether. An analogy can be made with the different times it takes a rowboat to travel two different round-trip paths in a river that flows at a
Consider a hypothetical force mediated by the exchange of bosons that have the same mass as protons. Approximately what would be the maximum range of such a force? You may assume that the total energy of these particles is simply the rest-mass energy and that they travel close to the speed of
A free neutron decays into a proton and an electron (and an anti-neutrino). A free proton has never been observed to decay. Why then do we consider the neutron to be as "fundamental" (at the nuclear level) a particle as the proton? Why do we not consider a neutron to be a proton-electron composite?
In a positron annihilation experiment, positrons are directed toward a metal. What are we likely to observe in such an experiment, and how might it provide information about the momentum of electrons in the metal?
If the energy of the virtual photon mediating an electron-proton scattering, e- + p → e- + p, is E, what is the range of this electromagnetic interaction in terms of E?
Figure 39.34 shows a Feynman diagram for the fundamental process involved in the decay of a free neutron: One of the neutrons down quarks converts to an up quark, emitting a virtual IV boson, which decays into an electron and an anti-electron-neutrino (the only decay energetically possible). Sketch
Does the decay process n → p + π- violate any conservation rules?
Consider the decay process π* → μ* + vμ + ve Can this decay occur?
Can the reaction π0 + n → K- + Σ+ occur?
How do we know for certain that the scattering process e* + vμ → e* + vμ proceeds through an intermediate Z boson and cannot proceed through an intermediate charged W boson, while both options are possible for e* + ve → e+ + ve?
A 4.50-MeV alpha particle is incident on a platinum nucleus (Z = 78). What is the minimum distance of approach, rmin?
A 6.50-MeV alpha particle is incident on a lead nucleus. Because of the Coulomb force between them, the alpha particle will approach the nucleus to a minimum distance, rmin. a) Determine rmin. b) If the kinetic energy of the alpha particle is increased, will the particle's distance of approach
A 6.50-MeV alpha particle scatters at a 60.0° angle off a lead nucleus. Determine the differential cross section of the alpha particle.
Protons with a kinetic energy of 2.00 MeV scatter off gold nuclei in a foil target. Each gold nucleus contains 79 protons. If both the incoming protons and the gold nuclei can be treated as point objects, what is the differential cross section that will cause the protons to scatter off the gold
The de Broglie wavelength, A, of a 5.00-MeV alpha particle is 6.40 fm, and the closest distance, rmin, to the gold nucleus this alpha particle can get is 45.5 fm (calculated in Example 39.1). How does the ratio rmim/λ vary with the kinetic energy of the alpha particle?
An experiment similar to the Geiger-Marsden experiment is done by bombarding a 1.00-p.m-thick gold foil with 8.00-MeV alpha particles. Calculate the fraction of particles scattered at an angle a) Between 5.00° and 6.00° and b) Between 30.0° and 31.0°. (The atomic mass number of gold is 197, and
The differential cross section that will cause particles to scatter at an angle 55° off a target is 4.0-10-18 m2/sr. A detector with an area of 1.0 cm2 is placed 1.0 m away from the target in order to detect particles that have been scattered at 55°. If 3.0-1017 particles hit the
Some particle detectors measure the total number of particles integrated over part of a sphere of radius R, where the target is at the center of the sphere. Assuming symmetry about the axis of the incoming particle beam, use the Rutherford scattering formula to obtain the total number of particles
Evaluate the form factor and the differential cross section, dσ/dΩ, tor a beam of electrons scattering off a uniform-density charged sphere of total charge Ze and radius R. Describe the scattering pattern.
A proton is made of two up quarks and a down quark (uud). Calculate its charge.
Use the fact that the observed magnetic moment of a proton is 1.4 ∙ 10-6 A m" to estimate the speed of its quarks. For this estimate, assume that the quarks move in circular orbits of radius 0.80 fm and that they all move at the same speed and direction. Ignore any relativistic effects.
Determine the approximate probing distance of a photon with an energy of 2.0 keV.
Draw a Feynman diagram for an electron-proton scattering, e- + p → e- + p, mediated by photon exchange.
Based on the information in Table 39.2, what is the approximate upper bound on the range of a reaction mediated by the Higgs boson?
Draw Feynman diagrams for the following phenomena: a) Protons scattering off each other b) A neutron beta decays to a proton: n → p + e- + e
A proton and a neutron interact via the strong nuclear force. Their interaction is mediated by a meson, much like the interaction between charged particles is mediated by photons-the particles ol the electromagnetic field.a) Perform a rough estimate of the mass of the meson from the uncertainty
How many fundamental fermions are there in a carbon dioxide molecule (CO2)?
Suppose a neutral pion at rest decays into two identical photons. a) What is the energy of each photon? b) What is the frequency of each photon? c) To what part of the electromagnetic spectrum do the photons correspond?
Draw a quark-level Feynman diagram for the decay of a neutral kaon into two charged pions: K0 → π+ + π-.
During the radiation-dominated era of the universe, the temperature was falling gradually according to equation 39.17. Using Stefan's Law, find the time dependence of background-radiation intensity during that era.
Use equation 39.17 to estimate the age of the universe when protons and neutrons began to form.
Three hundred thousand years after the Big Bang, the average temperature of the universe was about 3000 K. a) At what wavelength would the blackbody spectrum peak for this temperature? b) In what portion of the electromagnetic spectrum is this wavelength found?
At about 10"" s after the Big Bang, the universe had cooled to a temperature of approximately 1013 K. (a) Calculate the thermal energy kKT of the universe at that temperature. (b) Explain what happened to most of the hadrons-protons and neutrons-at that time. (c) Explain what happened to electrons
Three hundred thousand years after the Big Bang, the temperature of the universe was 3000 K. Because of expansion, the temperature of the universe is now 2.75 K. Modeling the universe as an ideal gas and assuming that the expansion is adiabatic, calculate how much the volume of the universe has
The fundamental observation underlying the Big Bang theory of cosmology is Edwin Hubbies 1929 discovery that the arrangement of galaxies throughout space is expanding. Like the photons of the cosmic microwave background, the light from distant galaxies is stretched to longer wavelengths by the
What is the minimum energy of a photon capable of producing an electron-positron pair? What is the wavelength of this photon?
a) Calculate the kinetic energy of a neutron that has a de Broglie wavelength of 0.15 nm. Compare this with the energy of an X-ray photon that has the same wavelength. b) Comment on how this energy difference is relevant to using neutrons or X-rays for investigating biological samples.
A photon can interact with matter by producing a proton-antiproton pair. What is the minimum energy the photon must have?
Suppose you had been doing an experiment to probe structure on a scale for which you needed electrons with 100. eV of kinetic energy. Then a neutron beam became available for the experiment. What energy would the neutrons need to have to give you the same resolution?
What is the de Broglie wavelength of an alpha particle that has a kinetic-energy of 100. MeV? According to Figure 39.13, how does this wavelength compare to the size of structure that can be probed with this alpha particle?
One of the elementary bosons that can mediate electroweak interactions is the Z0 boson, having the mass of 91.1876 GeV/c2. Find the order of magnitude of the range of the electroweak interaction.
What are the wavelengths of the two photons produced when a proton and an antiproton at rest annihilate?
Estimate the cross section of a Λ0 particle decay (into p + π-, n + π0) if the time it takes for this electroweak interaction to occur is ~ 10-10 s.
Determine the classical differential cross section for Rutherford scattering of alpha particles of energy 5.00 MeV projected at uranium atoms and scattered at an angle of 35.0° from the initial trajectory. Assume that both the target and the projectile atoms are point like.
The Geiger-Marsden experiment successfully demonstrated the existence of the nucleus and put limits on its size using the scattering of alpha particles from gold foils. Assume that the alpha particles were fired with a speed about 5.00% of the speed of light. a) Derive the upper bound of the radius
An electron-positron pair, traveling toward each other with a speed of 0.99c with respect to their center of mass, collide and annihilate according to e- + e+ → γ + γ. Assuming that the observer is at rest with respect to the center of mass of the electron-positron pair, what is the wavelength
Electron and positron beams are collided, and pairs of tau leptons are produced. If the angular distribution of the tau leptons varies as (1 + cos2 θ), what fraction of the tau lepton pairs will be captured in a detector that covers only the angles from 60° to 120°?
On July 4, 2012, the discovery of the Higgs boson at the Large Hadron Collider was announced. During the data-taking run, the I.HC reached a peak luminosity of 4.00 • 1033 cm-2 s-1 (this means that in an area of 1 square centimeter, 4.00-1033 protons collided every second). Assume that the cross
Evaluate the form factor and the differential cross section, dσ/dΩ, for a beam of electrons scattering off a thin spherical shell of total charge Ze and radius a. Could this scattering experiment distinguish between thin-shell and solid-sphere charge distributions? Explain.
A neutrino beam with E = 337 GeV is passed through a 68.5-cm-thick slab of aluminum-27 (with 27 nucleons in each nucleus). What fraction of the neutrinos will scatter off a nucleon if the cross section is given by σ(E) = (0.68∙10-38 cm2 GeV-1)E, (Aluminum has a density of 2.77 g/cm3.)
A neutrino beam with E = 143 GeV is passed through a slab of aluminum-27 (with 27 nucleons in each nucleus). The probability that a neutrino in the beam will scatter off a nucleon in the aluminum slab is 4.19 ∙ 10-12. The scattering cross section is given by σ(E) = (0.68 ∙10-38 cm2 GeV-1)E,
A high-energy neutrino beam is passed through a slab of aluminum-27 (with 27 nucleons in each nucleus) of thickness 71.1 cm. The probability that a neutrino in the beam will scatter off a nucleon in the aluminum slab is 6.00-10-12. The scattering cross section is given by σ(E) = (0.68∙10-38 cm2
A Geiger-Marsden experiment, in which alpha particles are scattered off a thin gold film, yields an intensity of I(94.9°) = 853 counts/s at a scattering angle of 94.9° ± 0.7°. What is the intensity (in counts/s) at a scattering angle of 60.5° ± 0.7° if the scattering obeys the Rutherford
A Geiger-Marsden experiment, in which alpha particles are scattered off a thin gold film, yields an intensity of I(95.1°) = 1129 counts/s at a scattering angle of 95.1° ± 0.4°. At a second scattering angle, the intensity is measured to be 4840 counts/s. Assuming that the scattering obeys the
A Geiger-Marsden experiment, in which alpha particles are scattered off a thin gold film, is set up with two detectors at θ1 = 85.1° ± 0.9° and θ2 = 62.9° ± 0.9°. Assuming that the scattering obeys the Rutherford formula, what is the ratio of the measured intensities, I1 / I2?
Which of the following reactions cannot occur, and why? a) p → π* + π° b) pπ° → n + e* c) Λ° (l116) → p + K-π* d) Λ° (1450) → p + K- + π*
Would neutron scattering or electromagnetic wave scattering (using X-rays or light) be more appropriate for investigating the scattering cross section of an atom as a whole? Which would be more appropriate for investigating the cross section of a nucleus of an atom? Which result will depend on /,
Why are there magic numbers in the nuclear shell model?
The binding energy of 32He is lower than that of, 31H. Provide a plausible explanation, taking into consideration the Coulomb interaction between two protons in 32He.
Some food is treated with gamma radiation to kill bacteria. Why is it not a concern that people who eat such food are ingesting gamma radiation?
Why are atomic nuclei more or less limited in size and in neutron-proton ratio? That is, why are there no stable nuclei with 10 times as many neutrons as protons, and why are there no atomic nuclei the size of marbles?
A nuclear reaction of the kind 32He + 126C → X + α is called a pick-up reaction. a) Why does it have this name, that is, what is picked up, what picked it up, and where did it come from? b) What is the resulting nucleus, X? c) What is the Q-value of this reaction? d) Is this reaction endothermic
Isospin, or isotopic spin, is a quantum variable describing the relationship between protons and neutrons in nuclear and particle physics. (Strictly, it describes the relationship between up and down quarks, as described in Chapter 39, but it was introduced before the advent of the quark model.) It
Before looking it up, predict intrinsic spin (i.e., actual angular momentum) of the deuteron, 21H. Explain your reasoning.
3918Ar is an isotope with a half-life of 269 yr. If it decays through β- decay, what isotope will result?
A neutron star is essentially a gigantic nucleus with mass 1.35 times that of the Sun, or a mass number of order 1057. It consists of approximately 99% neutrons, the rest being protons and an equal number of electrons. Explain the physics that determines these features.
Calculate the binding energies of the following nuclei. (a) 73Li (b) 126C (c) 5626Fe (d) 85379b
Give the numbers of protons, nucleons, neutrons, and electrons in an atom of 13454Xe.
Using the Fermi function, determine the relative change in density, (dn(r) / dr)/ n0, at the nuclear surface, r = R(A).
Calculate the binding energy for the following two uranium isotopes (where u = 1.66∙10-27 kg):(a) 23892U, which consists of 92 protons, 92 electrons, and 146 neutrons, with a total mass of 238.0507826 u(b) 23592U, which consists of 92 protons, 92 electrons, and 143 neutrons, with a total mass of
Write equations for the fi decay of the following isotopes: (a) 6027Co (b) 31H (c) 146C
Write equations for the alpha decay of the following isotopes: a) 21286Rn b) 24195Am

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