![Physics for Scientists and Engineers With Modern Physics](https://www.bartleby.com/isbn_cover_images/9781133953982/9781133953982_largeCoverImage.gif)
Physics for Scientists and Engineers With Modern Physics
9th Edition
ISBN: 9781133953982
Author: SERWAY, Raymond A./
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
Chapter 41, Problem 5OQ
To determine
The position where the particle is most likely to be found.
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
=
Consider a particle with mass m in an infinite square well of width L = 1, with energy E
(a) What energy state n is this particle in?
(b) What is the probability that the particle is in the range
Assume that an atomic nucleus can be thought of as a three-dimensional box with a width of 2 x 10^-14 m. If a proton moving as particles in this box, specify : Energy is excited first and second.
An electron in a one-dimensional region of length L is described by the wavefunction ψn(x) = sin(nπx/L), where n = 1, 2, …, in the range x = 0 to x = L; outside this range the wavefunction is zero. The orthogonality of these wavefunctions is confirmed by considering the integralI= ∫0L sin(nπx/L)sin(mπx/L)dx(a) Use the identity sinAsinB = 1/2{cos(A-B)-cos(A+B)} to rewrite the integrand as a sum of two terms. (b) Consider the case n = 2, m = 1, and make separate sketch graphs of the two terms identified in (a) in the range x = 0 to x = L. (c) Make use of the properties of the cosine function to argue that the area enclosed between the curves and the x axis is zero in both cases, and hence that the integral is zero. (d) Generalize the argument for the case of arbitrary n and m (n ≠ m).
Chapter 41 Solutions
Physics for Scientists and Engineers With Modern Physics
Ch. 41.1 - Prob. 41.1QQCh. 41.2 - Prob. 41.2QQCh. 41.2 - Prob. 41.3QQCh. 41.5 - Prob. 41.4QQCh. 41 - Prob. 1OQCh. 41 - Prob. 2OQCh. 41 - Prob. 3OQCh. 41 - Prob. 4OQCh. 41 - Prob. 5OQCh. 41 - Prob. 6OQ
Ch. 41 - Prob. 7OQCh. 41 - Prob. 8OQCh. 41 - Prob. 9OQCh. 41 - Prob. 10OQCh. 41 - Prob. 1CQCh. 41 - Prob. 2CQCh. 41 - Prob. 3CQCh. 41 - Prob. 4CQCh. 41 - Prob. 5CQCh. 41 - Prob. 6CQCh. 41 - Prob. 7CQCh. 41 - Prob. 8CQCh. 41 - Prob. 1PCh. 41 - Prob. 2PCh. 41 - Prob. 3PCh. 41 - Prob. 4PCh. 41 - Prob. 5PCh. 41 - Prob. 6PCh. 41 - Prob. 7PCh. 41 - Prob. 8PCh. 41 - Prob. 9PCh. 41 - Prob. 10PCh. 41 - Prob. 11PCh. 41 - Prob. 12PCh. 41 - Prob. 13PCh. 41 - Prob. 15PCh. 41 - Prob. 16PCh. 41 - Prob. 17PCh. 41 - Prob. 18PCh. 41 - Prob. 19PCh. 41 - Prob. 20PCh. 41 - Prob. 21PCh. 41 - Prob. 22PCh. 41 - Prob. 23PCh. 41 - Prob. 24PCh. 41 - Prob. 25PCh. 41 - Prob. 26PCh. 41 - Prob. 27PCh. 41 - Prob. 28PCh. 41 - Prob. 29PCh. 41 - Prob. 30PCh. 41 - Prob. 31PCh. 41 - Prob. 32PCh. 41 - Prob. 33PCh. 41 - Prob. 34PCh. 41 - Prob. 36PCh. 41 - Prob. 37PCh. 41 - Prob. 38PCh. 41 - Prob. 39PCh. 41 - Two particles with masses m1 and m2 are joined by...Ch. 41 - Prob. 41PCh. 41 - Prob. 42PCh. 41 - Prob. 43APCh. 41 - Prob. 44APCh. 41 - Prob. 45APCh. 41 - Prob. 46APCh. 41 - Prob. 47APCh. 41 - Prob. 48APCh. 41 - Prob. 49APCh. 41 - Prob. 50APCh. 41 - Prob. 51APCh. 41 - Prob. 52APCh. 41 - Prob. 53APCh. 41 - Prob. 54APCh. 41 - Prob. 56APCh. 41 - Prob. 57APCh. 41 - Prob. 58APCh. 41 - Prob. 59CPCh. 41 - Prob. 60CPCh. 41 - Prob. 61CPCh. 41 - Prob. 62CPCh. 41 - Prob. 63CP
Knowledge Booster
Similar questions
- Is it possible that when we measure the energy of a quantum particle in a box, the measurement may return a smaller value than the ground state energy? What is the highest value of the energy that we can measure for this particle?arrow_forwardAn electron is trapped in a one-dimensional box that is 501 nm wide. Initially, it is in the n = 3 energy level but, after a photon is absorbed, the electron is in the n = 6 energy level. What was the wavelength of the absorbed photon? wavelength: .0306 Eventually, the electron ends up in the ground state. As it does so, one or more photons are emitted during those transitions. Find the wavelengths of the least energetic and most energetic photons that might be emitted during all the possible transitions to the ground state. wavelength of least energetic photon: wavelength of most energetic photon: Incorrect m Incorrect m Earrow_forwardIf the speed of a proton is measured to be 2.9 × 105 m/s with a precision of 0.70% then what is the maximum precision with which its position could be measured, Ax? How does this uncertainty compare to the size of the proton?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_forwardAn 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?arrow_forward7. A particle confined to move on a sphere is in the state ) = N(2|31) - i|1, -1) + |30) - 3|21)) (a) What are the possible measurements of energy and what are the probabilities of finding them? (b) What are the possible measurements of L₂, and what are the probabilities of finding them?arrow_forward
- 1) An electron is confined to a square box of length L, and the walls of that box are infinitely high. The zero-point energy (ZPE) is defined as the minimal energy that corresponds to the smallest quantum number n. What would be the length of the box L such that the ZPE of the electron located inside this box is equal to its rest mass energy mec2?arrow_forward21. A particle with mass m is confined in a finite square well with the same height and length of 6E1-IDW. The particle has a ground state energy of E1-IDW = 3.57EV. If the particle transitioned from the second excited state to the first excited state, what is the wavelength of the photon emitted? (Note that Uo = 6E1-DW.) Consider replacing the system with a harmonic oscillator potential with angular frequency o = 1.25 x 1015 rad/s? What is the wavelength of the emitted photon if the particle transitions from the second excited state to the first excited state? State (n) Finite Square Well 1 0.625 E1-IDW 2 2.43 E1-IDW 5.09 E1-IDWarrow_forwardConsider an electron in a 1D box (0 ≤ x ≤ L, L = 1 nm) (a) Plot the wavefunctions as a function of x for n = 1,2,3,4. (b) Plot the probability densities for position for these wavefunctions. (c) To excite the particle from the ground state to the second excited state using light. What is the wavelength of the light? (d) What are the possible momenta for each state? (e) Consider n = 3, what is the probability of obtaining each specific momentum in a measurement?arrow_forward
- Consider an electron in a 1D box (0 ≤ x ≤ L, L = 1 nm)(a) Plot the wavefunctions as a function of x for n = 1, 2, 3, 4.(b) Plot the probability densities for position for these wavefunctions.(c) To excite the particle from the ground state to the second excited state using light. What is the wavelength of the light?(d) What are the possible momenta for each state?(e) Consider n = 3, what is the probability of obtaining each specific momentum in a measurement?PS. as there is no wave function provided in the homework question, Ive done the part (a) and i think it should be Ψ=sqrt(2/L)sin(nπx/L). hope it would help. thanks!!arrow_forwardChapter 39, Problem 029 An electron (mass m) is contained in a cubical box of widths Ly = Ly = Lz = L. It emits and absorbs light by making transitions among the lowest five energy levels. (a) How many different frequencies of light could the electron emit or absorb if it makes a transition between a pair of the lowest five energy levels? What multiple of h/8mL2 gives the (b) lowest, (c) second lowest, (d) third lowest, (e) highest, (f) second highest, and (g) third highest frequency? (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units (g) Number Unitsarrow_forwardEstimate the lifetime of a state that gives rise to a line of width (a) 0.10 cm-1, (b) 1.0 cm-1, (c) 1.0 GHz.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 LearningUniversity Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStax
![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/9781938168185/9781938168185_smallCoverImage.gif)
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax