Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 39: Q. 6 (page 1136)

FIGURE Q39.6 shows wave packets for particles 1, 2, and 3. Which particle can have its velocity known most precisely? Explain.

Short Answer

Expert verified

The velocity of particle 1 is the most exact.

Step by step solution

01

Given information

Given: Graphs for wave functions of each particle.

02

Which particle has most precise wavelength.

When compared to particle 1, the wave functions of particles 2 and 3 are less spatially stretched. The more specific the position is known, the less precise the momentum is known, according to Heisenberg's Uncertainty Principle. Particles 2 and 3 have more exact position because their wave functions are less spatially stretched, but they have less precise momentum.

The most exact momentum belongs to particle 1.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

FIGURE Q39.4 shows the dot pattern of electrons landing on a screen. a. At what value or values of x is the electron probability density at maximum? Explain. b. Can you tell at what value or values of x the electron wave function c1x2 is most positive? If so, where? If not, why not?

A small speck of dust with mass 1.0×10-13ghas fallen into the hole shown in FIGURE P39.46 and appears to be at rest. According to the uncertainty principle, could this particle have enough energy to get out of the hole? If not, what is the deepest hole of this width from which it would have a good chance to escape?

FIGURE P39.32 shows |ψ(x)|2for the electrons in an experiment.

a. Is the electron wave function normalized? Explain.

b. Draw a graph of ψ(x)over this same interval. Provide a numerical scale on both axes. (There may be more than one acceptable answer.)

c. What is the probability that an electron will be detected in a 0.0010-cm-wide region atx=0.00cm? At x=0.50cm? At x=0.999cm?

d. If 104electrons are detected, how many are expected to land in the interval -0.30cm≤x≤0.30cm?

The wave function of a particle is

ψx=b1+x2-1mm≤x<0mmc1+x20mm≤x≤1mm

and zero elsewhere

shows the probability density for finding a particle at position x. a. Determine the value of the constant a, as defined in the figure. b. At what value of x are you most likely to find the particle? Explain. c. Within what range of positions centered on your answer to part b are you 75% certain of finding the particle? d. Interpret your answer to part c by drawing the probability density graph and shading the appropriate region.
See all solutions

Recommended explanations on Physics Textbooks

Space Physics

Read Explanation

Fields in Physics

Read Explanation

Electrostatics

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Force

Read Explanation

Thermodynamics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free