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 17CQ
Is it possible to measure energy of
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
1.
A particle of mass m is in the state
Y(r, t) = Ac 25
= Ac 25
where A and w are positive real constants and i= v-1.
For what time-intependent potential energy function V(x) does Y satisfy the Schrödinger equation
for a particle of mass m?
(Simply plug the Y you are given into the time-dependent Schrödinger equation:
h a?¥(x,t)
aY(x,t)
ih
at
+V(x)¥(x,t) ,
2m
take the space and time derivatives and solve for V(x).]
Consider a quantum mechanical ideal harmonic oscillator having a zero point energy of 1.4*10^-20J. how much energy could be released if the oscillator makes a transition from n=4 to n=2 states?
a)0.69*10^19J
b)2.88*10^-20J
c)5.76*10^20J
d)none are correct
According to the quantum mechanical postulates, the following graph shows:
V(x)
y(x)
(a)
(c)
OA. One well behaved and acceptable wave function.
B. Two well behaved and acceptable wave functions.
OC. Two unacceptable wave functions.
D. Four unacceptable wave functions.
y(x)
(b)
pů
u
V(x)
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
This problem considers energy and work aspects of Example 10.7—use data from that example as needed. (a) Calcul...
College Physics
The electromagnetic spectrum of light is often arranged in terms of frequency. Which one of the following has t...
Lecture- Tutorials for Introductory Astronomy
1. A cyclist goes around a level, circular track at constant speed. Do you agree or disagree with the following...
College Physics: A Strategic Approach (4th Edition)
1. A person gets in an elevator on the ground floor and rides it to the top floor of a building. Sketch a veloc...
College Physics: A Strategic Approach (3rd Edition)
Atmospheric pressure exerts a large force (equal to the weight of the atmosphere above your body—about 10 tons)...
University Physics Volume 1
16. (II) A golf ball of mass 0.045 kg is hit off the lee at a speed of 38 m/s. The golf club was in contact wit...
Physics: Principles with Applications
Knowledge Booster
Similar questions
- (a) If the position of a chlorine ion in a membrane is measured to an accuracy of 1.00 m, what is its minimum uncertainty in velocity, given its mass is 5.8601026 kg? (b) If the ion has this velocity, what is its kinetic energy in eV, and how does this compare with typical molecular binding energies?arrow_forwardThe kinetic energy operator in 3-D is: O a. O b. Î=- T= OCT=- O d. T= ħ 2m ħ 2m 2 2 ħ 2m ħ 2m D2 D2 For a given quantum particle (p²)=a²ħ² and : = 0. The uncertainty in momentum for this particle is: ○a. a ²ħ² Ob.aħ О с. 2а ћ O d.-aħarrow_forward2. What is the magnetic dipole moment of a sphere of uniform surface charge density o, which rotates with constant angular velocity o about an axis of the sphere? An electron has a permanent magnetic dipole moment of magnitude: eħ (Bohr magneton). 2mc u = Suppose the electron is a rotating spherical shell of charge with "classical electron radius": e? mc What is the velocity at the equator? Can classical electrodynamics explain the origin of the electron magnetic moment?arrow_forward
- 22. Using the normalization condition, show that the constant A has the value (ma/ħn)/4 for the one- dimensional simple harmonic oscillator in its ground state.arrow_forwardPlease asaparrow_forwardA quantum system has a ground state with energy Eo = 0 meV and a 2-fold degenerate excited state with energy E₁ = 50 meV. E1 Calculate the probability of finding the system in its ground state when it is at T = 300 K. Select one: O a. 0.78 O b. 0.22 O c. 1 O d. 0.87arrow_forward
- A harmonic oscillator transitions from the ground state to the third excited state. What is the ratio of the ground state energy with the energy of the third excited state, Eo/E3? A. 1 5 B. 1 C. 3 D. 3 I7 37 CT | CO 5arrow_forward1. Given the wavefunction p(x) = Axe-ax? that describes a state of a harmonic oscillator provided that the constant a chosen correctly. Using the potential for a harmonic oscillator 1 1 U(x) =Kx? =-mw?x? 2 2 where w = K (a) Determine the amplitude A. (b) Show that the Schrödinger equation is satisfied when a = and 2h energy E =hw.arrow_forwardA 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?arrow_forward
- a) Determine the quantum mechanical operators for the following: Lx = ypz - ZPy That is, find Îx = ŷpz - 2py where x = x êx = ħa i əx Ly = Zpx -xPz Ly = 2px - xpz ŷ = y Py = ћд і ду 2= Z Lz = xpy - ypx L₂ = xpy - ŷêx Pz = ћд і дzarrow_forwardA2. Angular momentum in quantum mechanics is given by Ĺ = Îçi+Îyj+Î₂k with components Îx = ÛÎz – ZÎy, Îy = ÊÎx − ÎÔz, Îz = ÎÎy – ÎÎx. (a) Use the known commutation rules for â, ŷ, ê, êr, Ây, and ôz to show that [Îy, Î₂] = iħÎx. 1 3 2√ 2π sin(0) exp(-io), where and o (b) Consider the spherical harmonic Y₁,-1(0, 0) = are the polar and azimuthal angles, respectively. (i) Express Y₁,-1 in terms of cartesian coordinates. (ii) Using this expression in cartesian coordinates, show that Y₁,-1 is an eigenfunction of Î₂. (c) A wavefunction of a particle moving in three spatial dimensions is given as (x, y, z) = cz exp[-√√x² + y² + 2²/(2a)], where c and ao are constants. Determine the constant ao so that this wavefunction solves the stationary Schrödinger equation for the potential energy V(x, y, z) e² 4πεονη2 + y? +arrow_forwardThe kinetic energy operator in 3-D is: O a. O b. 2 ħ Î=- 2m OCT= 2 ħ2 T= D2 2m ħ 2m 72 Odg=h? O d. T= 2m V =α For a given quantum particle (p²)=a²ħ² andarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
- University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStaxCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax CollegePrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
College Physics
Physics
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:OpenStax College
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning