Modern Physics
3rd Edition
ISBN: 9781111794378
Author: Raymond A. Serway, Clement J. Moses, Curt A. Moyer
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
Chapter 5, Problem 36P
To determine
The phase speed of matter wave associated with the free particle. Verify that the phase speed is different from the speed at which particle carry mass and energy.
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
A physicist makes many measurements of the frequency of light emitted when a electron transitions from a particular excited state of an ion. For the system she is studying, the only allowed transition from the excited state is to the ground state. Her measurements have an average value of favg=2.13×1015 Hz with a standard deviation of ?f=17.4×106 Hz.
What is the minimum lifetime Δtmin of the excited state in seconds?
A quantum particle of mass m is placed in a one-dimensional box of length L. Assume the box is so small that the particle’s motion is relativistic and K = p2/2m is not valid. (a) Derive an expression for the kinetic energy levels of theparticle. (b) Assume the particle is an electron in a box of length L = 1.00 × 10-12 m. Find its lowest possible kinetic energy. (c) By what percent is the nonrelativistic equation in error?
In quantum interpretation of the electromagnetic waves in vacuum the photon
has the energy E = hw/2n and the momentump= hk/2n. So the ratio
E
of the energy to the momentum is
= c, the speed of light in
k
vacuum.
Similar relation can be obtained in classical electrodynamics as follows.
Consider the time-averaged energy density of the electromagnetic field
ɛ = B² /2µ0 + €0 E² /2 for a plane wave propagating in vacuum along the
z-direction. Calculate the time-averaged energy flux (Poynting flux) for such a
wave S = E × H and confirm that its ratio to the time-averaged energy
density ratio is equal to the speed of light in vacuum, S/e = c.
Chapter 5 Solutions
Modern Physics
Ch. 5.1 - A 0.20-kg ball is thrown upward. How much work is...Ch. 5.5 - Prob. 5ECh. 5 - Prob. 1QCh. 5 - Prob. 2QCh. 5 - Prob. 3QCh. 5 - Prob. 4QCh. 5 - Prob. 5QCh. 5 - Prob. 7QCh. 5 - Prob. 8QCh. 5 - Prob. 9Q
Ch. 5 - Prob. 10QCh. 5 - Prob. 11QCh. 5 - Prob. 1PCh. 5 - Prob. 2PCh. 5 - Prob. 3PCh. 5 - Prob. 4PCh. 5 - Prob. 5PCh. 5 - Prob. 6PCh. 5 - Prob. 7PCh. 5 - Prob. 8PCh. 5 - Prob. 9PCh. 5 - Prob. 10PCh. 5 - Prob. 11PCh. 5 - Prob. 12PCh. 5 - Prob. 13PCh. 5 - Prob. 14PCh. 5 - Show that the group velocity for a nonrelativistic...Ch. 5 - Prob. 16PCh. 5 - Prob. 17PCh. 5 - Prob. 18PCh. 5 - Prob. 19PCh. 5 - Prob. 20PCh. 5 - Prob. 21PCh. 5 - Prob. 22PCh. 5 - Prob. 23PCh. 5 - Prob. 24PCh. 5 - Prob. 25PCh. 5 - Prob. 26PCh. 5 - Prob. 27PCh. 5 - Prob. 28PCh. 5 - Prob. 29PCh. 5 - Prob. 30PCh. 5 - Prob. 31PCh. 5 - Prob. 32PCh. 5 - Prob. 33PCh. 5 - Prob. 34PCh. 5 - Prob. 35PCh. 5 - Prob. 36PCh. 5 - Prob. 37P
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_forwardShow that the wave function in (a) Equation 7.68 satisfies Equation 7.61, and (b) Equation 7.69 satisfies Equation 7.63.arrow_forwardAn electron in a box is in the ground state with energy 2.0 eV. (a) Find the width of the box. (b) How much energy is needed to excite the electron to its first excited state? (c) If the electron makes a transition from an excited state to the ground state with the simultaneous emission of 30.0-eV photon, find the quantum number of the excited state?arrow_forward
- Can we simultaneously measure position and energy of a quantum oscillator? Why? Why not?arrow_forwardConsider a freely moving quantum particle with mass m and speed u. Its energy is E = K = 1/2mu2. (a) Determine the phase speed of the quantum wave representing the particle and (b) show that it is different from the speed at which the particle transports mass and energy.arrow_forwardQ 3: Two people measure a wave of a particle passing from a point in front of them and their measurements are as follows: First person: W, (x,t) = Acos(5x — 3t) Second person: W,(x,t) = Acos(5.1x — 3.2t) 1 Find the wave packet consisting of these two waves in its simplest form. 2 2-If you know that at time t = 0.1s in position x = 1m, The wave packet was ¥(x.t) = 7.9726375772 what is the value of the constant Aarrow_forward
- For a free relativistic quantum particle moving with speed u, the total energy of the particle is E = hf = hω = √p2c2 + m2c4 and the momentum is p = h/λ = hk = γmu. For the quantum wave representing the particle, the group speed is υg = dω/dk. Prove that the group speed of the wave is the same as the speed of the particle.arrow_forwardThe relation for total energy (E ) and momentum (p) for a relativistic particleis E 2 = c2 p2 + m2c4, where m is the rest mass and c is the velocity of light.Using the relativistic relations E = ω and p = k, where ω is the angularfrequency and k is the wave number, show that the product of group velocity(vg) and the phase velocity (vp) is equal to c2, that is vpvg = c2arrow_forwardQ#2 (a) The relation for total energy (E) and momentum (p) for a relativistic particle is E = c² p² + m²c*, where m is the rest mass and c is the velocity of light. Using the relativistic relations E = h w and p = hk, where w is the angular frequency and k is the wave number, show that the product of group velocity and the phase velocity is equal to c2.arrow_forward
- Starting with the wave function = ei(kx-wt) obtain the operators for kinetic energy and total energy?arrow_forwardQ 3: Two people measure a wave of a particle passing from a point in front of them and their measurements are as follows: First person: W, (x,t) = A cos(5x — 3t) Second person: ¥a(xt) = A cos(5.1x ~320) 1 Find the wave packet consisting of these two waves in its simplest form. 2 2-If you know that at time t = 0.1s in position x = 1m, The wave packet was ¥(x.t) = 7.9726375772 what is the value of the constant Aarrow_forwardA 4.00-g particle confined to a box of length L has a speed of 1.00 mm/s. (a) What is the classical kinetic energy of the particle? (b) If the energy of the first excited state (n = 2) is equal to the kinetic energy found in part (a), what is the value of L? (c) Is the result found in part (b) realistic? Explain.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Modern PhysicsPhysicsISBN:9781111794378Author:Raymond A. Serway, Clement J. Moses, Curt A. MoyerPublisher:Cengage Learning
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher: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
Glencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill
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
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
Glencoe Physics: Principles and Problems, Student...
Physics
ISBN:9780078807213
Author:Paul W. Zitzewitz
Publisher:Glencoe/McGraw-Hill