Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
expand_more
expand_more
format_list_bulleted
Question
Chapter 6, Problem 42E
(a)
To determine
The proof that
(b)
To determine
The proof that group velocity is equal to particle velocity.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
The velocity of an electron is measured to a precision of 62 × 10-³
m/s. What is the minimal uncertainty to which its position can be
measured?
Please give your answer in units of mm, accurate to one decimal place.
I.e, the answer you should enter should have the form: XX.X mm.
Answer:
P-8 Please help me with the below question clearly with step by step explanation, please.
Note: The algebra for this problem can be a bit much -- at the very least set up the equations and state what the knowns and unknowns are.
An unknown moving ion is confined in a OD nanomaterial in which all three dimensions
are equals to 5 nm. Estimate with what accuracy its velocity and energy can be
measured (given mass of the ion is 4.8×10 26 kg)?
Chapter 6 Solutions
Modern Physics
Ch. 6 - Prob. 1CQCh. 6 - Prob. 2CQCh. 6 - Prob. 3CQCh. 6 - Prob. 4CQCh. 6 - Prob. 5CQCh. 6 - Prob. 6CQCh. 6 - Prob. 7CQCh. 6 - Prob. 8CQCh. 6 - Prob. 9CQCh. 6 - Prob. 10CQ
Ch. 6 - The diagram below plots (k) versus wave number for...Ch. 6 - Prob. 12CQCh. 6 - Prob. 13ECh. 6 - Prob. 14ECh. 6 - Prob. 15ECh. 6 - Prob. 16ECh. 6 - Prob. 17ECh. 6 - Prob. 18ECh. 6 - Prob. 19ECh. 6 - Prob. 20ECh. 6 - Prob. 21ECh. 6 - Prob. 22ECh. 6 - Prob. 23ECh. 6 - Prob. 24ECh. 6 - Prob. 25ECh. 6 - Prob. 26ECh. 6 - Prob. 27ECh. 6 - Prob. 28ECh. 6 - Obtain the smoothness conditions at the...Ch. 6 - Prob. 30ECh. 6 - Prob. 31ECh. 6 - Jump to Jupiter The gravitational potential energy...Ch. 6 - Prob. 33ECh. 6 - Obtain equation (618) from (616) and (617).Ch. 6 - Prob. 35ECh. 6 - Prob. 36ECh. 6 - Prob. 37ECh. 6 - Prob. 38ECh. 6 - Prob. 39ECh. 6 - Prob. 40ECh. 6 - Prob. 41ECh. 6 - Prob. 42ECh. 6 - Prob. 43ECh. 6 - Prob. 44ECh. 6 - Prob. 45ECh. 6 - Prob. 46ECh. 6 - Prob. 47ECh. 6 - Prob. 48ECh. 6 - Prob. 49ECh. 6 - Prob. 50ECh. 6 - Prob. 51CECh. 6 - Prob. 52CECh. 6 - Prob. 53CECh. 6 - Prob. 54CECh. 6 - Prob. 56CE
Knowledge Booster
Similar questions
- Problem 3. Consider the two example systems from quantum mechanics. First, for a particle in a box of length 1 we have the equation h² d²v EV, 2m dx² with boundary conditions (0) = 0 and V(1) = 0. Second, the Quantum Harmonic Oscillator (QHO) = h² d² +kr²V = EV 2m dg²+ka² 1/ k2²) v (a) Write down the states for both systems. What are their similarities and differences? (b) Write down the energy eigenvalues for both systems. What are their similarities and differences? (c) Plot the first three states of the QHO along with the potential for the system. (d) Explain why you can observe a particle outside of the "classically allowed region". Hint: you can use any state and compute an integral to determine a probability of a particle being in a given region.arrow_forwardProve that the thermal conductivity could also be written as: neKB 3KBT m Where KB denotes the Boltzmann constant and m denotes the electron ng the expression of the electric conductivity o previously established he problem, prove that the Lorentz number is given by: 2 Steam Heat flow T- OT 2 E+ OT dx A dE dx 3 (KBY == { B E Figure 2 T-(17) E C E- 1 dE dx Candarrow_forward2-13. Show that for a particle confined to a cube of length a that 2 E, Ps 3 V By taking the ensemble average of both sides, we have 2 E 3 V If we use the fact that E = }NkT, we get the ideal gas equation of state.arrow_forward
- Quantum Mechanics: please explain clearly with reasoning/steps Q1) "~P(x,0) = [Ax Ах 04x49/2/2 2 A(a-x) a≤x≤a a) SKETCH + (x₁0) AND EXPLAIN WHY: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_forwardAn electron is revolving around a proton in a circular orbit of radius r. The proton is assumed to be stationary. The total energy of this system is p2 E e2 2m 4T€, r where p and m denote the momentum and mass of the electron, respectively. Take the radius r to be an estimate of the uncertainty in position Ar, and the uncertainty in momentum Ap to be an estimate of p. Suppose that ArAp involving only m, e, ħ, and €o. Give the numerical value for E1 in electronvolts. Discuss if your results are consistent with Bohr's model for the hydrogen atom. h when the system is in the ground state. Obtain the expression for the ground state energy E1,arrow_forward
- Determine the probability distribution function in the phase space for a relativistic particle in a volume V and with energy ε(p) = √√√/m²c²+p²c², where p is the ab- solute value of the momentum, m the mass, and c the speed of light. Give the final result in terms of the modified Bessel functions r+∞ Ky (z) = ™ (v-1)! 2 -zcosht e cosh (vt) dt Ky(z) ~ Check what happens in the limit ² →0. mc² kT z 0.arrow_forwardA scientist has devised a new method of isolating individual particles. He claims that this method enables him to detect simultane- ously the position of a particle along an axis with a standard deviation of 0.12 nm and its momentum component along this axis with a stan- dard deviation of 3.0 * 10-25 kg m/s. Use the Heisenberg uncertainty principle to evaluate the validity of this claimarrow_forwardAssuming that the radius of the circular path of the electron is 4.9cm when voltage is 100v and coil current is 1A and The Helmholtz coils have 130 turns and a radius of 15 cm. With N=130 and R=0.15 What is the velocity of the electrons at 100 V, assuming the known charge and mass of the electron from the accepted universal constants that are the basis of SI units? Hints: Do a classical calculation of the kinetic of the electon assuming you know its mass (in kg) and its charge (in coulomb). That will be 1/2 mv2. Equate that to the energy of the electron gained by accelerating in the electric field, that is, eV where "e" is the charge and "V" is the difference potential in volts. Solve for "v", the velocity. Enter your answer in km/s, 103 m/s, without units. It is best to enter only a number, without an "e". For example, if you found 2000 m/s you would enter "2" for the velocity in km/s. Electrons have low mass and achieve high velocity in modest fields.arrow_forward
- Now let's try it with the momentum. The necessary partial derivatives are: ӘР ар Ovr = mi What's the uncertainty in the momentum SP? ?m - V1 ӘР ?uz - m2 aP ?mz = 02arrow_forwardConsider a model thermodynamic assembly in which the allowed one-particle states have energies 0, ?, 2?, 3?, 4?,5?,6?,.... The assembly has three particles and a total energy of 7?. Identify the possible particle number distributions and calculate the average distribution of the three particles in the energy states when the particles are (a) localized and distinguishable (b) gaseous bosons (c) gaseous fermionsarrow_forward
arrow_back_ios
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 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