/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q. 19 An electron confined in a harmon... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 40: Q. 19 (page 1175)

An electron confined in a harmonic potential well emits a 1200nm photon as it undergoes a 3鈫�2quantum jump. What is the spring constant of the potential well?

Short Answer

Expert verified

Spring constant of potential well =2.243N/m

Step by step solution

01

Step 1. Given information

Energy levels of quantum harmonic oscillator,

En=n-12鈩�蝇

Here,

ndenotes the state,

鈩�=reduced Planck's constant and

蝇=classical angular frequency.

02

Step 2. Energy of second level and third level

for second level,

E2=2-12鈩�蝇

=32鈩�蝇

for third level,

E3=3-12鈩�蝇

=52鈩�蝇

螖E3鈫�2=E3-E2

=52鈩�蝇-32鈩�蝇

=鈩�蝇

03

Step 3. For classical angular frequency

Ephoton=hc位photon

螖E3鈫�2=hc位photon

therefore,

h蝇=hc位photon

h蝇2蟺=hc位photon

蝇=2蟺c位photon

蝇=(2蟺)3脳108m/s1200nm10-9m1.0nm

=18.84脳108m/s1.2脳10-6m

=15.7脳1014s-1

04

Step 4. Finding spring constant

蝇=km

km=蝇2

k=m蝇2

k=9.1脳10-31kg2.5脳1014s-12

=2.243N/m

Thus, the spring constant of potential well=2.243N/m

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.

Over 30 million students worldwide already upgrade their learning with 91影视!

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

A proton鈥檚 energy is 1.0MeV below the top of a 10fm-wide energy barrier. What is the probability that the proton will tunnel through the barrier?

An electron in a rigid box absorbs light. The longest wavelength in the absorption spectrum is600nm. How long is the box?

The graph in FIGURE EX40.16 shows the potential-energy function U(x of a particle. Solution of the Schr枚dinger 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.

a. Sketch graphs of the probability density 蠄x2for the four states in the finite potential well of Figure 40.14a. Stack them vertically, similar to the Figure 40.14a graph of 蠄x.

b. What is the probability that a particle in then=2 state of the finite potential well will be found at the center of the well? Explain.

c. Is your answer to part b consistent with what you know about standing waves? Explain.

A particle confined in a rigid one-dimensional box of length 10fmhas an energy level En=32.9MeVand an adjacent energy level En+1=51.4MeV.

a. Determine the values of n and n + 1.

b. Draw an energy-level diagram showing all energy levels from 1 through n + 1. Label each level and write the energy beside it.

c. Sketch the n + 1 wave function on the n + 1 energy level.

d. What is the wavelength of a photon emitted in the n+1鈫�ntransition? Compare this to a typical visible-light wavelength.

e. What is the mass of the particle? Can you identify it?
See all solutions

Recommended explanations on Physics Textbooks

Fundamentals of Physics

Read Explanation

Further Mechanics and Thermal Physics

Read Explanation

Electrostatics

Read Explanation

Energy Physics

Read Explanation

Medical Physics

Read Explanation

Classical Mechanics

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.