University Physics Volume 3
17th Edition
ISBN: 9781938168185
Author: William Moebs, Jeff Sanny
Publisher: OpenStax
expand_more
expand_more
format_list_bulleted
Textbook Question
Chapter 7, Problem 92CP
Use Heisenberg's uncertainty principle to estimate the ground state energy of a particle oscillating on an spring with angular frequency,
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A certain atom remains in an excited state for about 51.7 ns before emitting a 2.15-eV photon and transitioning to the ground state. What is the uncertainty in the frequency of the photon in Hz?
A quantum particle of mass m is placed in a one-dimensional box of length L. Assume the box is so small that the particle’s motion is relativistic and K = p2/2m is not valid. (a) Derive an expression for the kinetic energy levels of theparticle. (b) Assume the particle is an electron in a box of length L = 1.00 × 10-12 m. Find its lowest possible kinetic energy. (c) By what percent is the nonrelativistic equation in error?
A neutron of mass 1.675 × 10-27 kg has a de Broglie wavelength of 7.8x10-12 m. What is the kinetic energy (in eV) of this non-relativistic neutron? Please give your answer with two decimal places.
1 eV = 1.60 × 10-19 J, h = 6.626 × 10-34 J ∙ s.
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...
Additional Science Textbook Solutions
Find more solutions based on key concepts
A ball is kicked with an initial velocity of 16 m/s in the horizontal direction and 12 m/s in the vertical dire...
College Physics
The proton is a composite particle composed of three quarks, all of which are either up quarks (u; charge +23e)...
Essential University Physics: Volume 2 (3rd Edition)
A 120-kg astronaut is riding in a rocket sled that is sliding along an inclined plane. The sled has a horizonta...
University Physics Volume 1
The electromagnetic spectrum of light is often arranged in terms of frequency. Which one of the following has t...
Lecture- Tutorials for Introductory Astronomy
The force, when you push against a wall with your fingers, they bend.
Conceptual Physics (12th Edition)
39.(I) A stone is dropped from the top of a cliff. It is seen to hit the ground below after 3.55 s. How high is...
Physics: Principles with Applications
Knowledge Booster
Similar questions
- Suppose that we do not know quantum mechanics and that the electron of a hydrogen atom behaves like a harmonic oscillator with a certain oscillation frequency f. In this model, an excited electron can therefore emit light and this has the same frequency f as the oscillating motion of the electron.It is observed that the light emitted by such an atom has a frequency of 800 Hz and the oscillating movement of the electron has an amplitude of 0,418 nm. In electro-volts, what is its mechanical energy?arrow_forwardSuppose that we do not know quantum mechanics and that the electron of a hydrogen atom behaves like a harmonic oscillator with a certain oscillation frequency f. In this model, an excited electron can therefore emit light and this has the same frequency f as the oscillating motion of the electron.It is observed that the light emitted by such an atom has a frequency of 800 Hz and the oscillating movement of the electron has an amplitude of 0,418 nm. What is the value of the corresponding spring constant (if the electron were bound to the proton by a spring)?arrow_forwardIf an excited state of an atom has a lifetime of 3.0××10^−7 s, what is the minimum error associated with the measurement of the energy of this state? ΔE=____ ×10^−28 Jarrow_forward
- The relation for total energy (E ) and momentum (p) for a relativistic particleis E 2 = c2 p2 + m2c4, where m is the rest mass and c is the velocity of light.Using the relativistic relations E = ω and p = k, where ω is the angularfrequency and k is the wave number, show that the product of group velocity(vg) and the phase velocity (vp) is equal to c2, that is vpvg = c2arrow_forwardam. 06.arrow_forwardA rectangular object has length l=30.3±0.6, width w=17.9±0.2. What is the absolute uncertainties in length?arrow_forward
- Q#2 (a) The relation for total energy (E) and momentum (p) for a relativistic particle is E = c² p² + m²c*, where m is the rest mass and c is the velocity of light. Using the relativistic relations E = h w and p = hk, where w is the angular frequency and k is the wave number, show that the product of group velocity and the phase velocity is equal to c2.arrow_forwardUsing the Bohr model, calculate the speed of the electron when it is in the first excited state, n = 2. The Bohr radius ₁ 5.29 x 10-11 m. Assume the electron is non-relativistic.arrow_forward8. Classical Mechanics. The differential equation for the velocity v of an object of mass m, restricted to vertical motion and subject only to the forces of gravity and air resistance, is dv (1) m -mg - yv. dt In Eq. (i) we assume that the drag force, -yu where y> 0 is a drag coefficient, is proportional to the velocity. Acceleration due to gravity is denoted by g. Assume that the upward direction is positive. (a) Show that the solution of Eq. (i) subject to the initial condition v(0) = vo is mg mg V= vo + mo) e e-rt/m Y (b) Sketch some integral curves, including the equilibrium solution, for Eq. (i). Explain the physical significance of the equilibrium solution. (c) If a ball is initially thrown in the upward direction so that vo > 0, show that it reaches its maximum height when m Yvo t = tmax (1 + Y mg -Inarrow_forward
- The velocity of an electron moving in the +x direction with a velocity of 0.12 c is measured with 1% precision. Find the uncertainty in the position of this electron using the uncertainty principle. warrow_forwardIn 2019, the International Committee for Weights and Measures adopted a new set of definitions for the fundamental units of the SI system. The three important base units in classical mechanics are the unit of time (s), the unit of length (m), and the unit of mass (kg). These three units are derived from three physical constants in the new SI system: Quantity Symbol Units Transition Frequency of Cesium 133 Av s-1 kg - m?/s m/s Planck's Constant h Speed of Light Use dimensional analysis to determine the combination of these three parameters that will define the base units of the SI system. (a) What combination of h, c, and Av defines a second? (b) What combination of h, c, and Av defines a meter? (c) What combination of h, c, and Av defines a kilogram? You only need to find the combination of h, c, and Av that has the right units. Your answer should not involve any numerical values.arrow_forwardConsider an anisotropic 3D harmonic oscillator where we = Wy the energy of the particle in the following state (nx, ny, n₂) = (0, 0, 2)? = w and wz A. 4ħw B. 6hw C. 3ħw D. 2.5ħw = 2w. What isarrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStaxPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning