Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 40: Q. 43 (page 1177)

Showed that a typical nuclear radius is 4fm As you’ll learn in Chapter 42, a typical energy of a neutron bound inside the nuclear potential well isEn=-20MeV. To find out how “fuzzy” the edge of the nucleus is, what is the neutron’s penetration distance into the classically forbidden region as a fraction of the nuclear radius?

Short Answer

Expert verified

The neutron’s penetration distance into the classically forbidden region as a fraction of the nuclear radius is1.02fm.

Step by step solution

01

Given Information

We need to find the neutron’s penetration distance into the classically forbidden region as a fraction of the nuclear radius.

02

Simplify

The distance ηis given as the equation:

η=h2mU0-E

Since the neutron's energy is 20MeVunder U0, so the U0-Ehas a value of 20MeV, and the distance is:

η=1.05×10-34Js21.67×10-27kg20×106eV×1.6×10-19JeVη=1.2×10-15m=1.02fm

The penetration distance is 25%of the nuclear radius.

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

For the quantum-well laser of Figure 40.16, estimate the probability that an electron will be found within one of the GaAlAs layers rather than in the GA As layer. Explain your reasoning.

The graph in FIGURE EX40.16 shows the potential-energy function U(x of a particle. Solution of the Schrödinger equation finds that the n=3 level has E3=0.5eVand that the n=6 level has E6=2.0eV.

a. Redraw this figure and add to it the energy lines for the n=3 and n=6 states.

b. Sketch the n=3 and n=6 wave functions. Show them as oscillating about the appropriate energy line.

The electrons in a rigid box emit photons of wavelength1484nmduring the3s2 transition.

a. What kind of photons are they—infrared, visible, or ultraviolet?

b. How long is the box in which the electrons are confined.

Rank in order, from largest to smallest, the penetration distancesηatoηcof the wave functions corresponding to the three energy levels in FIGURE Q40.5.

In most metals, the atomic ions form a regular arrangement called a crystal lattice. The conduction electrons in the sea of electrons move through this lattice. FIGURE CP40.47is a one-dimensional model of a crystal lattice. The ions have mass m, charge eand an equilibrium separation b.

a. Suppose the middle charge is displaced a very small distance x≪bfrom its equilibrium position while the outer charges remain fixed. Show that the net electric force on the middle charge is given approximately by

F=−e2b3πε0x

In other words, the charge experiences a linear restoring force.

b. Suppose this crystal consists of aluminum ions with an equilibrium spacing of 0.30nm. What are the energies of the four lowest vibrational states of these ions?

c. What wavelength photons are emitted during quantum jumps between adjacent energy levels? Is this wavelength in the infrared, visible, or ultraviolet portion of the spectrum?
See all solutions

Recommended explanations on Physics Textbooks

Physical Quantities And Units

Read Explanation

Work Energy and Power

Read Explanation

Rotational Dynamics

Read Explanation

Physics of Motion

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Electromagnetism

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