Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
Chapter 39, Problem 32P
(a)
To determine
The phase speed of matter wave associated with the free particle.
(b)
To determine
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
Consider 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.
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?
Q#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.
Chapter 39 Solutions
Physics for Scientists and Engineers with Modern Physics
Ch. 39.1 - Prob. 39.1QQCh. 39.2 - Prob. 39.2QQCh. 39.2 - Prob. 39.3QQCh. 39.2 - Prob. 39.4QQCh. 39.3 - Prob. 39.5QQCh. 39.5 - Prob. 39.6QQCh. 39.6 - Prob. 39.7QQCh. 39 - Prob. 1PCh. 39 - Prob. 2PCh. 39 - Prob. 3P
Ch. 39 - Prob. 4PCh. 39 - Prob. 5PCh. 39 - Prob. 6PCh. 39 - Prob. 8PCh. 39 - Prob. 9PCh. 39 - Prob. 10PCh. 39 - Prob. 11PCh. 39 - Prob. 12PCh. 39 - Prob. 13PCh. 39 - Prob. 15PCh. 39 - Prob. 16PCh. 39 - Prob. 17PCh. 39 - Prob. 18PCh. 39 - Prob. 19PCh. 39 - Prob. 20PCh. 39 - Prob. 22PCh. 39 - Prob. 23PCh. 39 - Prob. 24PCh. 39 - Prob. 25PCh. 39 - Prob. 26PCh. 39 - Prob. 27PCh. 39 - Prob. 30PCh. 39 - Prob. 31PCh. 39 - Prob. 32PCh. 39 - Prob. 33PCh. 39 - Prob. 35PCh. 39 - Prob. 37PCh. 39 - Prob. 38PCh. 39 - Prob. 39PCh. 39 - Prob. 40APCh. 39 - Prob. 41APCh. 39 - Prob. 43APCh. 39 - Prob. 44APCh. 39 - Prob. 45APCh. 39 - Prob. 46APCh. 39 - Prob. 47CPCh. 39 - Prob. 48CPCh. 39 - Prob. 49CPCh. 39 - Prob. 50CP
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_forwardGive at least one argument in support of the matter-wave hypothesis.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_forward
- What is the de Brogue wavelength of an electron travelling at a speed of 5.0106 m/s ?arrow_forwardCan we simultaneously measure position and energy of a quantum oscillator? Why? Why not?arrow_forwardCan the de Broglie wavelength of a particle be known precisely? Can the position of a particle be known precisely?arrow_forward
- Show that if the uncertainty in the position of a particle is on the order of its de Broglie's wavelength, then the uncertainty in its momentum is on the order of the value of its momentum.arrow_forwardIn 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.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_forward
- assume that an electron is moving along the x-axis and that you measure its speed to be 20.5*10^6m/s, which can be known with of precision of 0.50%. what is the minimum uncertainty (as allowed by the uncertainty principle in quantum theory )with which you can simultaneously measure the position of the electron along the x-axis?arrow_forwardA measurement is made of a photon’s energy (from a laser) that results in an uncertainty in the momentum of 6.63 × 10‒26 kg m/s. What is the uncertainty in the position of the photon?arrow_forwardStarting with the wave function = ei(kx-wt) obtain the operators for kinetic energy and total energy?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: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher: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