Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 4: Q8CQ (page 134)

Question: When we refer to a “bound” particle, we usually mean one for which there is no probability of finding it outside some finite confines. Could a bound particle be perfectly dead stationary, meaning a well-defined velocity of zero? Why or why not?

Short Answer

Expert verified

Answer:

No, according to the uncertainty relation, if ∆p=0then ∆xhas to be infinity, however, this can’t occur with a particle in a box that has definite uncertainty in the position.

Step by step solution

01

Uncertainty relation

Mathematically, the uncertainty relation can be stated as ΔxΔp⩾h2.

02

Explanation

The uncertainty connection does not permit this, though. The positional uncertainty of a particle contained in a box is known, but since the particle is stationary means∆p=0 , the positional uncertainty is unknown indefinitely ∆x=∞.

As a result, being stationary and being enclosed in a box cannot happen at the same time.

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

The p0 is a subatomic particle of fleeting existence. Data tables don't usually quote its lifetime. Rather, they quote a "width," meaning energy uncertainty, of about 150MeV. Roughly what is its lifetime?

Electrons are accelerated through a 20 V potential difference producing a monoenergetic beam. This is directed at a double-slit apparatus of 0.010 mm slit separation. A bank of electron detectors is 10 m beyond the double slit. With slit 1 alone open, 100 electrons per second are detected at all detectors. With slit 2 alone open, 900 electrons per second are detected at all detectors. Now both slits are open.

(a) The first minimum in the electron count occurs at detector X. How far is it from the center of the interference pattern?

(b) How many electrons per second will be detected at the center detector?

(c) How many electrons per second will be detected at detector X?

A mosquito of mass 0.15mgis found to be flying at a speed of 50cm/swithin an uncertainty of 0.5mm/s.(a) How precisely may its position be known? (b) Does this inherent uncertainty present any hindrance to the application of classical mechanics?

A beam of electrons strikes a crystal at an angleθwith the atomic planes, reflects of many atomic planes below the surface, and then passes into a detector also making angleθwith the atomic planes. (a) If the minimumθgiving constructive interference is.35° What is the ratioλ/d, Where is the spacing between atomic planes? (b) At what other angles, if any, would constructive interference occur?

An electron in an atom can "jump down" from a higher energy level to a lower one, then to a lower one still. The energy the atom thus loses at each jump goes to a photon. Typically, an electron might occupy a level for a nanosecond. What uncertainty in the electron's energy does this imply?
See all solutions

Recommended explanations on Physics Textbooks

Physics of Motion

Read Explanation

Radiation

Read Explanation

Modern Physics

Read Explanation

Scientific Method Physics

Read Explanation

Rotational Dynamics

Read Explanation

Translational Dynamics

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