University Physics Volume 3
17th Edition
ISBN: 9781938168185
Author: William Moebs, Jeff Sanny
Publisher: OpenStax
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Textbook Question
Chapter 7, Problem 14CQ
Using the quantum particle in a box model, describe how the possible energies of the particle are related to the size of the box.
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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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Similar questions
- Is it possible that when we measure the energy of a quantum particle in a box, the measurement may return a smaller value than the ground state energy? What is the highest value of the energy that we can measure for this particle?arrow_forwardAt what velocity does a proton have a 6.0-fm wavelength (about the size of a nucleus)? Give your answer in units of c.arrow_forwardIf the energy of the first excited state of the electron in the box is 25.0 eV, what is the width of the box?arrow_forward
- (a) Use the Heisenberg uncertainty principle to calculate the uncertainty in energy for a corresponding time interval of (b) Compare this energy with the unificationofforces energy and discuss why they are similar.arrow_forwardUse Heisenberg's uncertainty principle to estimate the ground state energy of a particle oscillating on an spring with angular frequency, =k/m, where k is the spring constant and m is the mass.arrow_forwardWhat are the dilemmas that come with the advancement of particle and quantum physics? The answers can be connected to the Large Hadron Collider. Please explain each dilemma.arrow_forward
- Radius of an atomic nucleus is of the order 2.2 fm. What is the minimum energy that an electron should have to be found inside the atomic nucleus? Is this possible in reality? Explain.arrow_forwardAfter studying the Large Hadron Collider technology, what are the dilemmas that come with the advancement of particle and quantum physics?arrow_forwardHow does the uncertainty principle apply to a known stable atomic system that apparently has an infi nite lifetime? How well can we know the energy of such a system?arrow_forward
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