Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 5, Problem 17CQ
To determine
Whether there is a minimum and a maximum wavelength of a photon for an infinite well, a harmonic oscillator and a hydrogen atom.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The Einstein's model makes the assumption that a solid can be treated a set of N identical, independent
harmonic oscillators. Compute the heat capacity for such a system. Make the simplifying assumption that a single
harmonic oscillator is described by the quantized energy levels: E, = kħw, where k = 0,1, 2, ....
Here are the properties of the GaAs quantum well in the figure.
v0 = 100 ??? L = 200 Å ?∗ = 0.067 m*
Find the energy values of the first three levels of this well. Corresponding wave functions Draw the graph. It is assumed that the effective mass m* given for the well is also valid for barriers. please. The material of the barrier is not important here. The important thing is the V0 potential.
An electron is trapped in a one-dimensional infinite potential well that is 100 pm wide; the electron is in its ground state. What is the probability that you can detect the electron in an interval of width x = 5.0 pm centered at x = (a) 25 pm, (b) 50 pm, and (c) 90 pm? (Hint: The interval x is so narrow that you can take the probability density to be constant within it.)
Chapter 5 Solutions
Modern Physics
Ch. 5 - Prob. 1CQCh. 5 - Prob. 2CQCh. 5 - Prob. 3CQCh. 5 - Prob. 4CQCh. 5 - Prob. 5CQCh. 5 - Prob. 6CQCh. 5 - Prob. 7CQCh. 5 - Prob. 8CQCh. 5 - Prob. 9CQCh. 5 - Prob. 10CQ
Ch. 5 - Prob. 11CQCh. 5 - Prob. 12CQCh. 5 - Prob. 13CQCh. 5 - Prob. 14CQCh. 5 - Prob. 15CQCh. 5 - Prob. 16CQCh. 5 - Prob. 17CQCh. 5 - Prob. 18CQCh. 5 - Prob. 19ECh. 5 - Prob. 20ECh. 5 - Prob. 21ECh. 5 - Prob. 22ECh. 5 - Prob. 23ECh. 5 - Prob. 24ECh. 5 - Prob. 25ECh. 5 - Prob. 26ECh. 5 - Prob. 27ECh. 5 - Prob. 28ECh. 5 - Prob. 29ECh. 5 - Prob. 30ECh. 5 - Prob. 31ECh. 5 - Prob. 32ECh. 5 - Prob. 33ECh. 5 - Prob. 34ECh. 5 - Prob. 35ECh. 5 - Prob. 36ECh. 5 - Prob. 37ECh. 5 - Prob. 38ECh. 5 - Prob. 39ECh. 5 - Prob. 40ECh. 5 - Prob. 41ECh. 5 - Prob. 42ECh. 5 - Obtain expression (5-23) from equation (5-22)....Ch. 5 - Prob. 44ECh. 5 - Prob. 45ECh. 5 - Prob. 46ECh. 5 - Prob. 47ECh. 5 - Prob. 48ECh. 5 - Prob. 49ECh. 5 - Prob. 50ECh. 5 - Prob. 51ECh. 5 - Prob. 52ECh. 5 - Prob. 53ECh. 5 - Prob. 54ECh. 5 - Prob. 55ECh. 5 - Prob. 56ECh. 5 - Prob. 57ECh. 5 - Prob. 58ECh. 5 - Prob. 59ECh. 5 - Prob. 60ECh. 5 - Prob. 61ECh. 5 - Prob. 62ECh. 5 - Prob. 63ECh. 5 - Prob. 64ECh. 5 - Prob. 65ECh. 5 - Prob. 66ECh. 5 - Prob. 67ECh. 5 - Prob. 68ECh. 5 - Prob. 69ECh. 5 - Prob. 70ECh. 5 - Prob. 71ECh. 5 - In a study of heat transfer, we find that for a...Ch. 5 - Prob. 73CECh. 5 - Prob. 74CECh. 5 - Prob. 75CECh. 5 - Prob. 76CECh. 5 - Prob. 77CECh. 5 - Prob. 78CECh. 5 - Prob. 79CECh. 5 - Prob. 80CECh. 5 - Prob. 81CECh. 5 - Prob. 82CECh. 5 - Prob. 83CECh. 5 - Prob. 84CECh. 5 - Prob. 85CECh. 5 - Prob. 86CECh. 5 - Prob. 87CECh. 5 - Prob. 88CECh. 5 - Consider the differential equation...Ch. 5 - Prob. 90CECh. 5 - Prob. 91CECh. 5 - Prob. 92CECh. 5 - Prob. 93CECh. 5 - Prob. 94CECh. 5 - Prob. 95CECh. 5 - Prob. 96CECh. 5 - Prob. 97CECh. 5 - Prob. 98CE
Knowledge Booster
Similar questions
- The wavefunction for the particle in a one-dimensional infinite potential well is given by V(x, t) = VI 2 e-iEnt/h En n?n?h? sin 2mL2 with 0arrow_forwardYour answer is partially correct. The ground-state energy of an electron trapped in a one-dimensional infinite potential well is 2.0 eV. What will this quantity be if the width of the potential well is multiplied by 6? Number 5.555 Units eVarrow_forwardConsider an 8-nm thick Ino.2Gao.8As quantum well with an infinite potential barrier. (a) Determine the density of states for the first heavy hole subband. (b) Determine the minimum photon energy required to be absorbed by this quantum well.arrow_forwardConsider a three-dimensional infinite potential well with a quantized energy of Enn,n, %3D (n + ng + n). where n = 1,2,3, ..,n, = 1,2,3, .., n, = 1,2,3, and a represents the 2ma potential well width in the x, y, and z directions. i. The lowest energy level that the electron may occupy is ii. The values of (ng, ny, ng) for the next higher energy level that is above the lowest energy level can be iii. If the electron drops from the energy level in item (ii) to the energy level in item (i), what is the wavelength of a photon that may be emitted if the work function is 0.4 V? Assume a=0.1 iv. Let the wave function has the general form Y(x,y, z) Asin nyy sin sin The value of A would be, v. Let (n, = 2, n, = 2,n, = 2). What is the probability that an electron exists in the intervals Osxs 0sys and o s z s?arrow_forwardAn electron is trapped in a one-dimensional infinite potential well that is 470 pm wide; the electron is in its ground state. What is the probability that you can detect the electron in an interval of width &x = 5.0 pm centered at x = 260 pm? (Hint: The interval 8x is so narrow that you can take the probability density to be constant within it.) Number Unitsarrow_forwardAn electron bounces elastically in 1D between two infinite potential walls separated by a distance L. The electron is in its lowest possible energy state. (a) What is the energy of this state? (b) The separation between the walls is slowly (a.k.a. 'adiabatically') increased to 2L. That the process occurs slowly means that the electron slowly adapts to continue to occupy the ground state of this new well of width 2L. What is the change in energy that the electron experiences? (c) With the walls again at a distance of L, imagine now that the separation is abruptly increased from L to 2L. This means that, at the moment when the change is made, the wavefunction is unchanged for a L. Write a (normalized) expression for 1(x) at this very moment, and draw it for the interval x = [0, 2L]. What is the expectation value of the energy for this ₁(a)? I'm calling it 1(a) not (x) to make it clear that it represents the ground state. (d) Show that the above 1(r) is no longer a solution for the…arrow_forwardConsider a particle of spin 1/2 whose normalized quantum state is given by l6) = V 2.1.0, +) + / 2.1,1.-). |2, 1,0, +) + Calculate the expectation values as well as the corresponding probability if measured d)§., e) j², f).İ2.arrow_forwardAssume that an electron is confined in a one-dimensional quantum well with infinite walls, draw the wave functions for the first 3 levels, ψ1, ψ2, ψ3. Also, show the probability density functions corresponding to these three levels?arrow_forwardAn electron is trapped in a one-dimensional infinite potential well that is 430 pm wide; the electron is in its ground state. What is the probability that you can detect the electron in an interval of width &x = 5.0 pm centered at x = 260 pm? (Hint: The interval Sx is so narrow that you can take the probability density to be constant within it.) Number i Unitsarrow_forwardThe energy eigenvalues of a 3-dimensional infinite well of sides a, b, c is given by Enml (n2 + m² +P)Eo Here n, m, lequal to 1, 2, .and E, is a constant energy. If b= a, c = 4, the energy levels up to the fourth excited state level in terms of En are Select one: O a. 4, 6, 13, 14 O b. 3, 6, 9, 11, 12 C. 4, 6, 9, 11, 12 O d. 4, 7, 10, 12, 13 О е. 4, 7, 9, 13, 14arrow_forwardConsider an atomic nucleus to be equivalent to a onedimensional infinite potential well with L = 1.4 * 10-14 m, a typical nuclear diameter.What would be the ground-state energy of an electron if it were trapped in such a potential well? (Note: Nuclei do not contain electrons.)arrow_forwardOarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_iosRecommended textbooks for you
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax