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…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter22: Entropy And The Second Law Of Thermodynamics

Section: Chapter Questions

Problem 43PQ

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Consider a collision between cart A, moving at speed, and cart B, immobile. The masses of the carts are known, as well as their uncertainty. Friction is neglected. Using the conservation of energy theorem, program cells to predict the speed of sliders A and B after the collision as well as its uncertainty. mA=(0.47±0.05) kg mB=(0.47±0.06) kg vi A=(1.9±0.02) m/s
Consider a particle of mass m moving in a 2-dimensional rectangular box of sides La and Ly, with Le 2Ly. If we use the symbols E, to denote the energy of the ground state of the system, Ee1 the energy of the first excited state, Ee2 the energy of the second excited state, and Ee3 the energy of the third excited state, what are the numerical values of the ratios Ee1/Eg, Ee2/Eg, and Ee3/E,?
To estimate the velocity of a toy car you measure that it moves a distance of (20.0 +\- 0.03) meters in a time of (4.00 +\- 0.04) seconds. Use the rules for uncertainty propagation to obtain a value for the car’s associated uncertainty.
To estimate the velocity of a toy car you measure that it moves a distance of (20.0 +/- 0.03) meters in a time of (4.00 +\- 0.04) seconds. Use the rules for uncertainty propagation to obtain a value for the car’s velocity.
Lunar astronauts placed a series of cube reflectors on the Moon as part of an experiment to mea- sure the distance to the Moon with hyperaccuracy. Lasers were fired from an observatory in West Texas toward the Moon; they reflected off these cubes and returned to Earth. The time of arrival was measured by astronomers at the observatory. If the time for the round trip could be measured with an accuracy of 0.1 nanoseconds, what was the uncertainty in the measured distance to the Moon. Given that the semi-major axis of the Moon’s orbit is 3.84 x 108 km, what is the percent accuracy of these measurements?
A student performs the experiment and measures the distance between photogates: d = 50 ± 0.1 cm, the times measured by photogates: t0 = 0.052 ± 0.001s and t1 = 0.035 ± 0.001s, and the cart’s length: s = 10 ± 0.05 cm. Find the acceleration a of the cart and estimate uncertainty in a.
A 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 claim
Show that for a system of N particles obeying M-B or classical statistics the average number of particles in the level j is given by Ñ, = -NKBT des F
When two galaxies collide, the stars do not generally run into eachother, but the gas clouds do collide, triggeering a burst of new star formation. a) Estimate the probability that our Sun would collide with another star in the Andromeda galaxy if a collision between the Milky Way and Andromeda occured. Assume that each galaxy has 100 billion stars exactly like the sun, spread evenly over a circular disk with a radius of 100,000 lightyears. (Hint: first calculate total area of 100 billion circles with the radius of the Sun and then compare that to total area to the area of the Galatic disk) b) Estimate the probability of a collision between a gas cloud in our galaxy and one in the Andromeda galaxy. Assume that each galaxy has 100,000 clouds of warm hydrogen gas, each with a radius of 300 lightyears, spread evenly over the same disk. Use the same method as part A.
View the particle system in a one-dimensional box in the range ≤ x ≤ of m-mass and q- charged particles. The system is then plagued with an electric field as a function of time t such that the potential energy of the fault can be expressed as 0 for t 0 with e amplitude of electric field Calculate the probability of transition from state n to state m as a time function t. And state which n-m transitions are allowed and not allowed to occur.
Check Your Understanding If a=3+4i , what is the product a* a?
Show that when 1(x,t) and 2(x,t) are solutions to the time-dependent Schrödinger equation and A, B are numbers then a function (x,t) that is a superposition of these functions is also a solution: (x,t)=A1(x,t)+B1(x,t).

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