For a system of particles of mass m in the state p the formula expression for theparticle flux vector in one dimension (number per unit time through a unit areaperpendicular to the direction of the motion of ) ishF =peaxax4πimShow that, for a beam of free particles moving with velocity v in one dimension,the expression givesF = v x density of particles

Given that :F=h4πimΨ* ∂Ψ∂x-Ψ∂Ψ*∂xNow, as we know that the wavefunction of a free particle…

Answered: For a system of particles of mass m in…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Similar questions

Why is the following situation impossible? An air rifle is used to shoot 1.00-g particles at a speed of υx = 100 m/s. The rifle’s barrel has a diameter of 2.00 mm. The rifle is mounted on a perfectly rigid support so that it is fired in exactly the same way each time. Because of the uncertainty principle, however, after many firings, the diameter of the spray of pellets on a paper target is 1.00 cm.
Protons of energy 5.1 MeV are incident on a silver foil of thickness 3.6 x 10-6 m. What fraction of the incident protons is scattered at the following angles? (The density of silver is 10.5 g/cm³, and its molar mass is 107.9 g/mol. Give your answer in decimal notation, e.g., 0.05 for 1/20.) (a) greater than 90° 3.716E-5 X (b) less than 5⁰
A three-dimensional wave function of a particle is u(x)=c/r exp(-kr/i)calculate the probability currentdensity
A proton is confined in a uranium nucleus of diameter 7.2 x 10-15 m. Use the energy-level calculation of a one-dimensional box that has length equal to the nuclear diameter to calculate the proton's minimum kinetic energy. What is the proton's minimum kinetic energy according to the uncertainty principle?
A particle has a lifetime of 1 × 10–23s. Calculate the typical uncertainty in themeasurement of its rest energy.
a) Write down an expression for the probability density ρ(t, x) of a particle described by the wavefunction Ψ(t, x). b) Using the probability density, explain how you would calculate the probability of finding this particle in the interval between x = A and x = B.
Consider a proton (m = 1.6726219 × 10-27 kg) confined in a box of length 10.000 pm. What is the energy difference between the n = 1 and n = 2 states of the proton-in-a-box? Report your answer in units of 10-18 J (that is, if the energy is 5.00 × 10-18 J, you would report it as "5.00").
= 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
Statistical Mechanics. We have a system of N bosons with zero spin. Each boson can have two states of energies 0 and E. Let μ be the chemical potential of the system and suppose that N >> 1. a) Determine the temperature T so that the mean population of the ground state is twice that of the excited state of energy E. Express kT only in terms of N and E. b) What would be the corresponding temperature T′ if the particles obeyed Boltzmann statistics? Compare both results and discuss them physically.
Can you solve this? With draw an illustration of the given situation below then solve the problem.
A system with 3 (three) indistinguishable particles has five energy states: E1 = 0, E2 = E, E3 = 2E, E4 = 3E, E5 = 4E. Determine the possible formation if it satisfies Bose- Einstein stats?
A 4.70-g particle confined to a box of length L has a speed of 4.40 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? m (c) Is the result found in part (b) realistic? Yes No Explain.

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