EP PHYSICS F/SCI.+ENGR.W/MOD..-MOD MAST
4th Edition
ISBN: 9780133899634
Author: GIANCOLI
Publisher: PEARSON CO
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 38, Problem 34P
(a)
To determine
The wavelength of electron in free space.
(b)
To determine
The wavelength of electron when over the well.
(c)
To determine
The diagram showing potential energy and total energy as function of
Expert Solution & Answer
![Check Mark](/static/check-mark.png)
Want to see the full answer?
Check out a sample textbook solution![Blurred answer](/static/blurred-answer.jpg)
Students have asked these similar questions
2) The energy levels of a quantum-mechanical, one-dimensional, anharmonic oscillator maybe
approximated as
2
=(n
* (n + )'
En
hw ;n = 0,1,2,...
(++) =
The parameter x, usually « 1, represents the degree of anharmonicity. Show that, to the first
order in x and the fourth order in u (= ħw/kgT), the specific heat of a system of N such
oscillators is given by
C = Nk [(1-u² + *)+ 4x (: + *)].
240
80
Note that the correction term here increases with temperature.
(10) i) Use the quantum mechanical kinetic energy operator T, =
to find the kinetic energy of the first
2m dx?
excited state of the Particle in a Box (with n = 2). ii) Then, use the relationship of kinetic energy and momentum (KE
= p?/2m) to find an equation for the de Broglie wavelength of the particle in a one-dimensional box as a function only
of the box length L and quantum number n. iii) Sketch the wavefunction in the box to verify that the expression you
obtained in part ii) is correct.
What do we need to do to average over Θ and ф to get the probability that the electron is inside a shell of radius r and thickness dr?
Chapter 38 Solutions
EP PHYSICS F/SCI.+ENGR.W/MOD..-MOD MAST
Ch. 38.3 - Prob. 1AECh. 38.8 - Prob. 1BECh. 38.8 - Prob. 1CECh. 38.9 - Prob. 1DECh. 38 - Prob. 1QCh. 38 - Prob. 2QCh. 38 - Prob. 3QCh. 38 - Prob. 4QCh. 38 - Would it ever be possible to balance a very sharp...Ch. 38 - Prob. 6Q
Ch. 38 - Prob. 7QCh. 38 - Prob. 8QCh. 38 - Prob. 9QCh. 38 - Prob. 10QCh. 38 - Prob. 11QCh. 38 - Prob. 12QCh. 38 - Prob. 13QCh. 38 - Prob. 14QCh. 38 - Prob. 15QCh. 38 - Prob. 16QCh. 38 - Prob. 17QCh. 38 - Prob. 18QCh. 38 - Prob. 1PCh. 38 - Prob. 2PCh. 38 - Prob. 3PCh. 38 - Prob. 4PCh. 38 - Prob. 5PCh. 38 - Prob. 6PCh. 38 - Prob. 7PCh. 38 - Prob. 8PCh. 38 - Prob. 9PCh. 38 - Prob. 10PCh. 38 - Prob. 11PCh. 38 - Prob. 12PCh. 38 - Prob. 13PCh. 38 - Prob. 14PCh. 38 - Prob. 15PCh. 38 - Prob. 16PCh. 38 - Prob. 17PCh. 38 - Prob. 18PCh. 38 - Prob. 19PCh. 38 - Prob. 20PCh. 38 - Prob. 21PCh. 38 - Prob. 22PCh. 38 - Prob. 23PCh. 38 - Prob. 24PCh. 38 - Prob. 25PCh. 38 - Prob. 26PCh. 38 - Prob. 27PCh. 38 - Prob. 28PCh. 38 - Prob. 29PCh. 38 - Prob. 30PCh. 38 - Prob. 31PCh. 38 - Prob. 32PCh. 38 - Prob. 33PCh. 38 - Prob. 34PCh. 38 - Prob. 35PCh. 38 - Prob. 36PCh. 38 - Prob. 37PCh. 38 - Prob. 38PCh. 38 - Prob. 39PCh. 38 - Prob. 40PCh. 38 - Prob. 41PCh. 38 - Prob. 42PCh. 38 - Prob. 43PCh. 38 - Prob. 44PCh. 38 - Prob. 45PCh. 38 - Prob. 46GPCh. 38 - Prob. 47GPCh. 38 - Prob. 48GPCh. 38 - Prob. 49GPCh. 38 - Prob. 50GPCh. 38 - Prob. 51GPCh. 38 - Prob. 52GPCh. 38 - Prob. 53GPCh. 38 - Prob. 54GPCh. 38 - Prob. 55GPCh. 38 - Prob. 56GPCh. 38 - Prob. 57GPCh. 38 - Prob. 58GPCh. 38 - Prob. 59GP
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Can the magnitude of a wave function (*(x,t)(x,t)) be a negative number? Explain.arrow_forwardSuppose a wave function is discontinuous at some point. Can this function represent a quantum state of some physical particle? Why? Why not?arrow_forwardWhen a quantum harmonic oscillator makes a transition from the (n+1) state to the n state and emits a 450-nm photon, what is its frequency?arrow_forward
- 3) Assume a one-dimension step potential with electrons described by free electron wave in positive x-direction in region I coming from the left towards the step edge. propagating V Vo || X Assume the energy E of the electron is 4 eV in region I and the potential is V₁-2 eV. Calculate the probability of finding an electron in regions I and II as a function of x.arrow_forwardThe wave function of an electron confined in a one-dimensional infinite potential well of width L is $₁₂(x)=√ √ √ ²/1₁ sin( -), 2 NTX L where n is a positive integer. If the electron is in the n = 5 state: i) Calculate the probability of finding the electron between x = L and x = L. ii) Calculate the probability of finding the electron in an interval of width 0.04L located at = = }L. xarrow_forwardConsider an electron, a proton, and an alpha particle (a helium nucleus), each trapped separately in identical boxes. (i) Which particle corresponds to the highest ground-state energy? Also which particle have longest wavelength when system is in ground statearrow_forward
- 1) A laser produces light of wavelength 525 nmnm in an ultrashort pulse. What is the minimum duration of the pulse if the minimum uncertainty in the energy of the photons is 1.0%%? Express your answer with the appropriate units.arrow_forwardAt what radius in Angstroms does the probability of finding an electron at a point in the ground state H atom fall to 70 per cent of its maximum value? (ans. in Angstroms)arrow_forward(100) An clectron is confined to a region of space that is L distance long (this is the "particle in a box" problem discussed in class). Draw a diagram of the allowed wave functions for the electron's first four energy levels. Also draw the square of the wave functions on your diagram. What are the wavelengths of each of these wave functions? n = 4 E4 n = 3 Ез E2 E, For the fourth energy level, what is the probability of finding the clectron in the far left quarter of the box?arrow_forward
- The planes of atoms in a particular cubic crystal lie parallel to the surface, 0.80 nm apart. X rays having wavelength 0.50 nm are directed at an angle θ to the surface. (a) For what values of θ will there be a strong refl ection? (b) What energy electrons could give the same result?arrow_forwardAn 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_forwardFor an electron having a de Broglie wavelength of 0.167 nm (appropriate for interacting with crystal lattice structures that are about this size): (a) Calculate the electron’s velocity, assuming it is nonrelativistic. (b) Calculate the electron’s kinetic energy in eV.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 LearningModern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage LearningUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
- Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9781133104261/9781133104261_smallCoverImage.gif)
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9781111794378/9781111794378_smallCoverImage.gif)
Modern Physics
Physics
ISBN:9781111794378
Author:Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9781938168185/9781938168185_smallCoverImage.gif)
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
![Text book image](https://www.bartleby.com/isbn_cover_images/9781337553292/9781337553292_smallCoverImage.gif)
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning