Essential University Physics (3rd Edition)
3rd Edition
ISBN: 9780134202709
Author: Richard Wolfson
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question
Chapter 36, Problem 56P
(a)
To determine
The number of the electron in harmonic oscillator potential in its state of lowest energy, if its energy is
(b)
To determine
The energy of highest-energy electron.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
What is the ground-state energy of (a) an electron and (b) a proton if each is trapped in a one-dimensional infinite potential well that
is 273 pm wide?
(a) Number
8.083824566
Units
eV
(b) Number
4.401408127
Units
eV
We are going to use Heisenberg's uncertainty principle to estimate the ground-
state energy of hydrogen. In our model, the electron is confined in a one-
dimensional well with a length about the size of hydrogen, so that Ax = 0.0529
nm. Estimate Ap, and then assume that the ground-state energy is
roughly Ap2/2me. (Give your answer in Joules or electron-volts.)
An electron is trapped in a one-dimensional region
of length 1.00 x 10-10 m (a typical atomic diameter).
(a) Find the energies of the ground state and first two
excited states. (b) How much energy must be supplied
to excite the electron from the ground state to the sec-
ond excited state? (c) From the second excited state, the
electron drops down to the first excited state. How much
energy is released in this process?
Chapter 36 Solutions
Essential University Physics (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
- An 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 the quant numbers Nx and Ny, the allowed energies are given by E = H^2/8Me ( Nx^2/ Lx^2 + Ny^2/Ly^2) i) assuming Lx and Ly =L. Find the energies of the lowest for all energy levels of the electron ii) construct an energy level diagram for the electron and determine the energy difference between the second exited state and the ground state?arrow_forwardAn electron confined to a one-dimensional box of length is in its third energy state. What is the probability of finding the electron in the region x = 0 to x = {/4?|arrow_forwardAn electron is confined to a one-dimensional region in which its ground-state (n = 1) energy is 1.95 eV. What is the length L of the region? and what energy input is required to promote the electron to its first excited state?arrow_forward
- A LiBr molecule oscillates with a frequency of 1.7×1013 Hz. (a) What is the difference in energy in eV between allowed oscillator states? (b) What is the approximate value of n for a state having an energy of 1.0 eV?arrow_forwardAn electron in an infinite potential well (a box) makes a transition from the n = 3 level to the ground state and, in doing so, emits a photon with a wavelength of 20.9 nm. (a) How wide is this well? (b) What wavelength of the photon would it take to excite the electron from its original level to the next higher level?arrow_forwardAn electron is bound in a square well of depth U. = 6E1-Dw. What is the width of the well if its ground-state energy is 2.00 eV?arrow_forward
- A particle of mass m is moving in an infinite 1D quantum well of width L. y,(x) = J? sinx. sin nAx L (a) How much energy must be given to the particle so it can transition from the ground state to the second excited state? (b) If the particle is in the first excited state, what is the probability of finding the particle between x = and x = ;? 2.arrow_forwardImpurities in solids can be sometimes described by a particle-in-a-box model. Suppose He is substituted for Xe, and assume a particle-in-a-cubic-box model, the length of whose sides is equal to the atomic diameter of Xe (≈ 2.62 Å). Compute the lowest excitation energy for the He atom’s motion. (This is the energy difference between the ground state and the first excited state.)arrow_forwardSolid metals can be modeled as a set of uncoupled harmonic oscillators of the same frequency with energy levels given by En = ħwn n = 0, 1, 2,... where the zero-point energy (the lowest energy state) of each oscillator has been adjusted to zero for simplicity. In this model, the harmonic oscillators represent the motions of the metal atoms relative to one another. The frequency of these oscillators is low so that ħw = = 224 KB and the system vibrational partition function is given by 3N Z ² = la₁ - (1 1 e-0/T). (a) If the system contains one mole of atoms, find the average energy (in J) of this system at T= 172 K. (You can use = BkB.) T (b) What is the absolute entropy (in J/K) for this system? You can use either the Gibbs expression for S, or the system partition function to make this evaluation (they are equivalent, as your reading assignment indicates).arrow_forward
- An electron is confined to a one-dimensional infinite well 0.1 nm. wide. (a) Determine the deBroglie wavelength of the electron in the ground state. (b) What is the electron’s minimum kinetic energy? (c) What is the energy of the first excited state? (d) What energy is required to excite the electron from the ground state to the first excited state? (e) What wavelength photon would be emitted if the system were to de-excite from the first excited state to the ground state.arrow_forwardA LiBr molecule oscillates with a frequency of 1.7×1013 Hz. (a) What is the difference in energy in eV between allowed oscillator states? (b) What is the approximate value of n for a state having an energy of 1.0eV?arrow_forwardAn electron confined to a box has the ground state energy of 2.4 eV. What is the width of the box in units of nanometers?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning