/*! 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. 21 An electron is confined in a har... [FREE SOLUTION] | 91影视

91影视

Find study content
Learning Materials

Discover learning materials by subject, university or textbook.

Explanations

Textbooks
All Subjects

Anthropology

Archaeology

Architecture

Art and Design

Bengali

Biology

Business Studies

Greek

Chemistry

Chinese

Combined Science

Computer Science

Economics

Engineering

English

English Literature

Environmental Science

French

Geography

German

History

Hospitality and Tourism

Human Geography

Italian

Japanese

Law

Macroeconomics

Marketing

Math

Media Studies

Medicine

Microeconomics

Music

Nursing

Nutrition and Food Science

Physics

Polish

Politics

Psychology

Religious Studies

Sociology

Spanish

Sports Sciences

Translation

All Subjects

Biology

Business Studies

Chemistry

Combined Science

Computer Science

Economics

English

Environmental Science

Geography

History

Math

Physics

Psychology

Sociology
Features
Features

Discover all of these amazing features with a free account.

Flashcards

91影视 AI

Notes

Study Plans

Study Sets
What鈥檚 new?

Flashcards
Study your flashcards with three learning modes.

Study Sets
All of your learning materials stored in one place.

Notes
Create and edit notes or documents.

Study Plans
Organise your studies and prepare for exams.
91影视
Discover

All the hacks around your studies and career - in one place.

Find a degree

Magazine
Featured

Magazine
Trusted advice for anyone who wants to ace their studies & career.

The largest student job board with the most exciting opportunities.

Verified student deals from top brands.

Discover our mobile app to take your studies anywhere.

Learning Materials

Features

Discover

Chapter 40: Q. 21 (page 1175)

An electron is confined in a harmonic potential well that has a spring constant of $12.0 N / m$ . What is the longest wavelength of light that the electron can absorb?

Short Answer

Expert verified

The longest wavelength of the light that the electron can absorb= $519 n m$

Step by step solution

01

Step 1. Given information

Equation of energy of quantum harmonic oscillator,

$E_{n} = (n - \frac{1}{2}) 鈩� 蝇$

Here,

$鈩�$ =are the planks constant,

$蝇$ =angular frequency of oscillator,

$n =$ the integer, and

$E_{n}$ =energy of the harmonic oscillator.

02

Step 2. For the frequency of oscillations

Spring constant= $k = 蝇^{2} m$

Angular frequency $蝇 = 2 蟺 f$

$蝇^{2} = \frac{k}{m}$

$蝇 = \sqrt{\frac{k}{m}}$

$2 蟺 f = \sqrt{\frac{k}{m}}$

$f = \frac{1}{2 蟺} \sqrt{\frac{k}{m}}$

Here,

$m =$ mass of the electron,

$k =$ spring constant, and

$f =$ frequency of oscillations.

f = \frac{1}{2 (3.14)} \sqrt{\frac{12.0 N / m}{9.11 脳 10^{- 31} kg}}

$= 5.78 脳 10^{14} Hz$

03

Step 3. For the wavelength

$位_{longest} = \frac{c}{f}$

$位_{longest} = \frac{3.0 脳 10^{8} m / s}{5.78 脳 10^{14} Hz}$

$= 519 脳 10^{- 9} m$

$= 519 nm$

Therefore, the longest wavelength of the light that electron can absorb $= 519 nm$

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 $16 n m$ -long box has a thin partition that divides the box into a $4 n m$ -long section and a $12 n m$ -long section. An electron confined in the shorter section is in the $n = 2$ state. The partition is briefly withdrawn, then reinserted, leaving the electron in the longer section of the box. What is the electron鈥檚 quantum state after the partition is back in place?

Figure 40.27a modeled a hydrogen atom as a finite potential well with rectangular edges. A more realistic model of a hydrogen atom, although still a one-dimensional model, would be the electron + proton electrostatic potential energy in one dimension:

$U (x) = - \frac{e^{2}}{4 {蟺蔚}_{0} |x|}$

a. Draw a graph of U(x) versus x. Center your graph at $x = 0$ .

b. Despite the divergence at $x = 0$ , the Schr枚dinger equation can be solved to find energy levels and wave functions for the electron in this potential. Draw a horizontal line across your graph of part a about one-third of the way from the bottom to the top. Label this line $E_{2}$ , then, on this line, sketch a plausible graph of the $n = 2$ wave function.

c. Redraw your graph of part a and add a horizontal line about two-thirds of the way from the bottom to the top. Label this line $E_{3}$ , then, on this line, sketch a plausible graph of the $n = 3$ wave function.

Consider a quantum harmonic oscillator.

a. What happens to the spacing between the nodes of the wave function as |x| increases? Why?

b. What happens to the heights of the antinodes of the wave function as |x| increases? Why?

c. Sketch a reasonably accurate graph of the n=8 wave function of a quantum harmonic oscillator.

Sketch the $n = 8$ wave function for the potential energy shown in FIGURE EX40.14.

An electron in a rigid box absorbs light. The longest wavelength in the absorption spectrum is $600 n m$ . How long is the box?

See all solutions

Recommended explanations on Physics Textbooks

Modern Physics

Read Explanation

Electricity

Read Explanation

Circular Motion and Gravitation

Read Explanation

Rotational Dynamics

Read Explanation

Physics of Motion

Read Explanation

Wave Optics

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.