Essential University Physics: Volume 2 (3rd Edition)
3rd Edition
ISBN: 9780321976420
Author: Richard Wolfson
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 36, Problem 58P
(a)
To determine
The expression for the system of
N
electrons in a harmonic oscillator potential in its state of lowest energy if
n
is even.
(b)
To determine
The expression for the system of
N
electrons in a harmonic oscillator potential in its state of lowest energy if
n
is odd.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A particle of mass m is confined to a 3-dimensional box that has sides Lx,=L Ly=2L, and Lz=3L. a) Determine the sets of quantum numbers n_x, n_y, and n_z that correspond to the lowest 10 energy levels of this box.
A system of three identical distinguishable particles has energy 3ɛ. The single particle can take
discrete energies 0, &, 2, 3ɛ and so on. The average number of particles in the energy state & is
1.2
0.9
0.6
0.3
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
Chapter 36 Solutions
Essential University Physics: Volume 2 (3rd Edition)
Ch. 36.1 - Prob. 36.1GICh. 36.2 - Prob. 36.2GICh. 36.3 - Prob. 36.3GICh. 36.4 - Prob. 36.4GICh. 36.5 - Prob. 36.5GICh. 36 - Prob. 1FTDCh. 36 - Prob. 2FTDCh. 36 - Prob. 3FTDCh. 36 - Prob. 4FTDCh. 36 - Prob. 5FTD
Ch. 36 - Prob. 6FTDCh. 36 - Prob. 7FTDCh. 36 - Prob. 8FTDCh. 36 - Prob. 9FTDCh. 36 - Prob. 10FTDCh. 36 - Prob. 11FTDCh. 36 - Prob. 12FTDCh. 36 - What distinguishes a Bose-Einstein condensate from...Ch. 36 - Prob. 14ECh. 36 - Prob. 15ECh. 36 - Prob. 16ECh. 36 - Prob. 17ECh. 36 - Prob. 18ECh. 36 - Prob. 19ECh. 36 - Prob. 20ECh. 36 - Prob. 21ECh. 36 - Prob. 22ECh. 36 - Prob. 23ECh. 36 - Prob. 24ECh. 36 - Prob. 25ECh. 36 - Prob. 26ECh. 36 - Prob. 27ECh. 36 - Prob. 28ECh. 36 - Prob. 29ECh. 36 - Prob. 30ECh. 36 - Prob. 31ECh. 36 - Prob. 32ECh. 36 - Prob. 33ECh. 36 - Prob. 34PCh. 36 - Prob. 35PCh. 36 - Prob. 36PCh. 36 - Prob. 37PCh. 36 - Prob. 38PCh. 36 - Prob. 39PCh. 36 - Prob. 40PCh. 36 - Prob. 41PCh. 36 - Prob. 42PCh. 36 - Prob. 43PCh. 36 - Prob. 44PCh. 36 - Prob. 45PCh. 36 - Prob. 46PCh. 36 - Prob. 47PCh. 36 - Prob. 48PCh. 36 - Prob. 49PCh. 36 - Prob. 50PCh. 36 - Prob. 51PCh. 36 - Prob. 52PCh. 36 - Prob. 53PCh. 36 - Prob. 54PCh. 36 - Prob. 55PCh. 36 - Prob. 56PCh. 36 - Prob. 57PCh. 36 - Prob. 58PCh. 36 - Prob. 59PCh. 36 - Prob. 60PCh. 36 - Prob. 61PCh. 36 - Prob. 62PCh. 36 - Prob. 63PCh. 36 - Prob. 64PCh. 36 - Prob. 65PCh. 36 - Prob. 66PCh. 36 - Prob. 67PCh. 36 - Prob. 68PCh. 36 - Prob. 69PCh. 36 - Prob. 70PCh. 36 - Prob. 71PCh. 36 - Prob. 72PCh. 36 - Prob. 73PCh. 36 - Prob. 74PCh. 36 - Prob. 75PCh. 36 - Prob. 76PPCh. 36 - Prob. 77PPCh. 36 - Prob. 78PPCh. 36 - Prob. 79PP
Knowledge Booster
Similar questions
- A nanoparticle containing 6 atoms can be modeled approximately as an Einstein solid of 18 independent oscillators. The evenly spaced energy levels of each oscillator are 5e-21 J apart. Use k = 1.4e-23 J/K. When the nanoparticle's energy is in the range 5(5e-21) J to 9(5e-21) J, what is the approximate heat capacity per atom?arrow_forwardAn electron is confined to move in the xy plane in a rectangle whose dimensions are Lx and Ly. That is, the electron is trapped in a two dimensional potential well having lengths of Lx and Ly. In this situation, the allowed energies of the electron depend on two quantum numbers nx and ny and are given by E = h2/8me (nx2/Lx2 + ny2/Ly2)Using this information, we wish to find the wavelength of a photon needed to excite the electron from the ground state to the second excited state, assuming Lx = Ly = L. (a) Using the assumption on the lengths, write an expression for the allowed energies of the electron in terms of the quantumnumbers nx and ny. (b) What values of nx and ny correspond to the ground state? (c) Find the energy of the ground state. (d) What are the possible values of nx and ny for the first excited state, that is, the next-highest state in terms of energy? (e) What are the possible values of nx and ny for thesecond excited state?…arrow_forwardA proton is confined in box whose width is d = 750 nm. It is in the n=3 energy state. What is the probability that the proton will be found within a distance of d/n from one of the walls? [Hint: the average value sin^2x over one or more of its cycles is 1/2] PLEASE PLEASE include a sketch of U(x) and Ψ(x)arrow_forward
- A particle of mass m is under the central force created by the potential energy U(r)=A*r (A>0). The angular momentum of the particle is L (L is not equal to zero). Find the minimum energy E0 (m, A, L). Hint is given in the figurearrow_forwardAn electron outside a dielectric is attracted to the surface by a force, F = -A/x2, where x is the perpendicular distance from the electron to the surface, and A is a positive constant. Electrons are prevented from crossing the surface, as there aren't any quantum states in the dielectric for them to occupy. Suppose that the surface is infinite, so that the problem is 1-dimensional. Write the Schrodinger equation for an electron outside of the surface (x > 0) and determine the appropriate boundary condition at x = 0. Obtain a formula for the allowed energy levels of the system. (Hint: Compare the equation for the wave function Ψ(x) with that satisfied by the wave functinon u(r) = rR(r) for a hydrogenic atom.)arrow_forwardConsider an electron in the first excited state of a one-dimensional infinite square well of length L=1A°. Calculate the force on either wall during an impact by the electron. Answer Choices: a. 0354 CN 6. 0.245 L c. 0.121μN d. 0.482 ANarrow_forward
- A particle is in a box of length L. Suddenly, the length of the box is increased to 2L. What happens to the energy levels as shown? (a) nothing; they are unaffected. (b) They move farther apart. (c) They move closer together.arrow_forward▼ Part A For an electron in the 1s state of hydrogen, what is the probability of being in a spherical shell of thickness 1.00×10-2 ap at distance aB? ▸ View Available Hint(s) 15. ΑΣΦ ? Part B For an electron in the 1s state of hydrogen, what is the probability of being in a spherical shell of thickness 1.00×10-2 ag at distance ag from the proton? ▸ View Available Hint(s) [5] ΑΣΦ ? Submit Submitarrow_forwardConsider a one-dimensional square potential well with a width of L and depth Vo. An electron is confined within this potential well. a) Calculate the energy levels of the electron in terms of L and Vo. b) Determine the wavelength of the electron associated with its lowest energy state (n=1). c) If the potential well has the width of L=5nm and Vo=10eV, calculate the energy of the electron in its lowest energy state.arrow_forward
- A potential well has 4 energy levels as given here: Energy of the state (eV) 13 12 9 4 Suppose that there are three electrons in the well, and that the system is in the first excited state. If the system emits a photon, what energy could the photon have? O (a) 3 eV Ⓒ (b) 5 eV O (c) 4 eV O (d) 8 eV (e) 9 eV x X 0%arrow_forwardThe probability density function (PDF) for electrons to be detected on the x-axis between 0 nm and 1.0 nm is shown below. What is the probability of finding the electron between x = 0.5 nm and x = 1.0 nm? |w(x)* (nm') 2.0 1.0 0.5 x (nm) 1.0arrow_forwardA population inversion for two energy levels is often described by assigning a negative Kelvin temperature to the system. What negative temperature would describe a system in which the population of the upper energy level exceeds that of the lower level by 10% and the energy difference between the two levels is 2.26 eV?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStaxModern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningPrinciples 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 LearningPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
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
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning