University Physics Volume 3
17th Edition
ISBN: 9781938168185
Author: William Moebs, Jeff Sanny
Publisher: OpenStax
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Chapter 7, Problem 78AP
The mass of a
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Chapter 7 Solutions
University Physics Volume 3
Ch. 7 - Check Your Understanding If a=3+4i , what is the...Ch. 7 - Check Your Understanding Suppose that a particle...Ch. 7 - Check Your Understanding For the particle in the...Ch. 7 - Check Your Understanding A sodium atom nukes a...Ch. 7 - Check Your Understanding A particle With mass m is...Ch. 7 - Check Your Understanding Which of the following...Ch. 7 - Check your Understanding (a) Consider an infinite...Ch. 7 - Check Your Understanding The vibrational frequency...Ch. 7 - Check Your Understanding Find the expectation...Ch. 7 - Check Your Understanding A proton with kinetic...
Ch. 7 - What is the physical unit of a wave function,...Ch. 7 - Can the magnitude of a wave function (*(x,t)(x,t))...Ch. 7 - What kind of physical quamtity does a wave...Ch. 7 - What is the physical meaning of a wave function of...Ch. 7 - What is the meaning of the expression "expectation...Ch. 7 - If the formalism of quantum mechanics is 'more...Ch. 7 - Can the de Broglie wavelength of a particle be...Ch. 7 - Can we measure the energy of a free localized...Ch. 7 - Can we measure both the position and momentum of a...Ch. 7 - What is the difference between a wave function...Ch. 7 - If a quantum particle is in a stationary state,...Ch. 7 - Explain the difference between time-dependent and...Ch. 7 - Suppose a wave function is discontinuous at some...Ch. 7 - Using the quantum particle in a box model,...Ch. 7 - Is it possible that when we measure the energy of...Ch. 7 - For a quantum panicle in a box, the first excited...Ch. 7 - Is it possible to measure energy of 0.75h for a...Ch. 7 - Explain the connection between Planck's hypothesis...Ch. 7 - If a classical harmonic oscillator can at rest,...Ch. 7 - Use an example of a quantum particle in a box or a...Ch. 7 - Can we simultaneously measure position and energy...Ch. 7 - When an electron and a proton of the same kinetic...Ch. 7 - What decreases the tunneling probability most:...Ch. 7 - Explain the difference between a box-potential and...Ch. 7 - Can a quantum particle 'escape' from an infinite...Ch. 7 - A tunnel diode and a resonant-tunneling diode both...Ch. 7 - Compute |(x,t)|2 for the function (x,t)=(x)sint,...Ch. 7 - Given the complex-valued function...Ch. 7 - Which one of the following functions, and why,...Ch. 7 - A particle with mass m moving along the x-axis and...Ch. 7 - A wave function of a particle with mass m is given...Ch. 7 - A velocity measurement of an a-particle has been...Ch. 7 - A gas of helium atoms at 273 K is in a cubical...Ch. 7 - If the uncertainty in the y -component of a...Ch. 7 - Some unstable elementary particle has a rest...Ch. 7 - An atom in a metastable state has a lifetime of...Ch. 7 - Measurements indicate that an atom remains in an...Ch. 7 - Suppose an electron is confined to a region of...Ch. 7 - Combine Equation 7.17 and Equation 7.18 to show...Ch. 7 - Show that (x,t)=Aei(kwt) is a valid solution to...Ch. 7 - Show that (x,t)=Asin(kxt) and (x,t)=Acos(kxt) do...Ch. 7 - Show that when 1(x,t) and 2(x,t) are solutions to...Ch. 7 - A particle with mass m is described by the...Ch. 7 - Find the expectation value of the kinetic energy...Ch. 7 - Find the expectation value of the square of the...Ch. 7 - A free proton has a wave function given by...Ch. 7 - Assume that an electron in an atom can be treated...Ch. 7 - Assume that a proton in a nucleus can be treated...Ch. 7 - An electron confined to a box has the ground state...Ch. 7 - What is the ground state energy (in eV) of a...Ch. 7 - What is the ground state energy (in eV) of an a...Ch. 7 - To excite an election in a one-dimensional box...Ch. 7 - An electron confined to a box of width 0.15 nm by...Ch. 7 - If the energy of the first excited state of the...Ch. 7 - Suppose an electron confined to a emits photons....Ch. 7 - Hydrogen H2 molecules are kept at 300.0 K in a...Ch. 7 - An electron is confined to a box of width 0.25 nm....Ch. 7 - An electron in a box is in the ground state with...Ch. 7 - Show that the two lowest energy states of the...Ch. 7 - If the ground state energy of a simple harmonic...Ch. 7 - When a quantum harmonic oscillator makes a...Ch. 7 - Vibrations of the hydrogen molecule H2 can be...Ch. 7 - A particle with mass 0.030 kg oscillates back-and-...Ch. 7 - Find the expectation value x2 of the square of the...Ch. 7 - Determine the expectation value of the potential...Ch. 7 - Verify that given by Equation 7.57 is a solution...Ch. 7 - Estimate the ground state energy of the quantum...Ch. 7 - A mass of 0.250 kg oscillates on a spring with the...Ch. 7 - Show that the wave function in (a) Equation 7.68...Ch. 7 - A 6.0-eV electron impacts on a barrier with height...Ch. 7 - A 5.0-eV electron impacts on a barrier of with...Ch. 7 - A 12.0-eV electron encounters a barrier of height...Ch. 7 - A quantum particle with initial kinetic energy...Ch. 7 - A simple model of a radioactive nuclear decay...Ch. 7 - A muon, a quantum particle with a mass...Ch. 7 - A grain of sand with mass 1.0 mg and kinetic...Ch. 7 - Show that if the uncertainty in the position of a...Ch. 7 - The mass of a -meson is measured to be 770MeV/c2...Ch. 7 - A particle of mass m is confined to a box of width...Ch. 7 - A particle in a box [0; L] is in the third excited...Ch. 7 - A 0.20-kg billiard ball bounces back and forth...Ch. 7 - Find the expectation value of the position squared...Ch. 7 - Consider an infinite square well with wall...Ch. 7 - Consider an infinite square well with wall...Ch. 7 - Atoms in a crystal lattice vibrate in simple...Ch. 7 - A diatomic molecule behaves like a quantum...Ch. 7 - An electron with kinetic energy 2.0 MeV encounters...Ch. 7 - A beam of mono-energetic protons with energy 2.0...Ch. 7 - An electron in a long, organic molecule used in a...Ch. 7 - In STM, an elevation of the tip above the surface...Ch. 7 - If STM is to detect surface features with local...Ch. 7 - Use Heisenberg's uncertainty principle to estimate...Ch. 7 - Suppose an infinite square well extends from L/2...Ch. 7 - A particle of mass m confined to a box of width L...
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- If the rest energies of a proton and a neutron (the two constituents of nuclei) are 938.3 and 939.6 MeV, what is the difference in their mass in kilograms?arrow_forwardThe K0 meson is an uncharged member of the particle “zoo” that decays into two charged pions according to K0 → π+ + π−. The pions have opposite charges, as indicated, and the same mass, mπ = 140 MeV/c2. Suppose that a K0 at rest decays into two pions in a bubble chamber in which a magnetic field of 2.0 T is present (see Fig. P2.22). If the radius of curvature of the pions is 34.4 cm, find (a) the momenta and speeds of the pions and (b) the mass of the K0 meson.arrow_forwardThe primary decay mode for the negative pion is +v . (a) What is the energy release in MeV in this decay? (b) Using conservation of momentum, how much energy does each of the decay products receive, given the is at rest when it decays? You may assume the muon antineutrino is massless and has momentum p = E/c , just like a photon.arrow_forward
- An unstable particle, initially at rest, decays into a proton (rest energy 938.3 MeV) and a negative pion (rest energy 139.5 MeV). A uniform magnetic field of 0.250 T exists perpendicular to the velocities of the created particles. The radius of curvature of each track is found to be 1.33 m. What is the rest mass of the original unstable particle?arrow_forwardSuppose you are designing a proton decay experiment and you can detect 50 percent of the proton decays in a tank of water. (a) How many kilograms of water would you need to see one decay per month, assuming a lifetime of 1031 y? (b) How many cubic meters of water is this? (c) If the actual lifetime is 1033 y, how long would you have to wait on an average to see a single proton decay?arrow_forwardWhat is for a proton having amass energy of 938.3 MeV accelerated through an effective potential of 1.0 TV (teravolt)?arrow_forward
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- (a) Verify from its quark composition that the particle could be an excited state of the proton. (b) There is a spread of about 100 MeV in the decay energy of the interpreted as uncertainty due to its short lifetime. What is its approximate lifetime? (c) Does its decay proceed via the strong or weak force?arrow_forwardSome unstable elementary particle has a rest energy of 80.41 GeV and an uncertainty in rest energy of 2.06 GeV. Estimate the lifetime of this particle.arrow_forward(a) Estimate the mass of the luminous matter in the known universe, given there are 1011 galaxies, each containing 1011 stars of average mass 1.5 times that of our Sun. (b) How many protons (the most abundant nuclide) are there in this mates? (c) Estimate the total number of particles in the observable universe by multiplying the answer to (b) by two, since there is an electron for each proton, and then by 109, since there are far more particles (such as photons and neutrinos) in space than in luminous matter.arrow_forward
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