An electron confined to a one-dimensional box has energy levels given by the equation En=n2h2/8mL2 where n is a quantum number with possible values of 1,2,3,…;m is the mass of the particle; and L is the length of the box.   a. Calculate the energies of the n=1,n=2, and n=3 levels for an electron in a box with a length of 170 pm . b. Calculate the wavelength of light required to make a transition from n=1→n=2 and from n=2→n=3. c. In what region of the electromagnetic spectrum do these wavelengths lie? radio microwave infrared visible light ultraviolet X-ray gamma ray

Chemistry: An Atoms First Approach
2nd Edition
ISBN:9781305079243
Author:Steven S. Zumdahl, Susan A. Zumdahl
Publisher:Steven S. Zumdahl, Susan A. Zumdahl
Chapter2: Atomic Structure And Periodicity
Section: Chapter Questions
Problem 161CP: The figure below represents part of the emission spectrum for a one-electron ion in lhe gas phase....
icon
Related questions
Question

An electron confined to a one-dimensional box has energy levels given by the equation

En=n2h2/8mL2

where n is a quantum number with possible values of 1,2,3,…;m is the mass of the particle; and L is the length of the box.

 

a. Calculate the energies of the n=1,n=2, and n=3 levels for an electron in a box with a length of 170 pm .

b. Calculate the wavelength of light required to make a transition from n=1→n=2 and from n=2→n=3.

c.
In what region of the electromagnetic spectrum do these wavelengths lie?
radio
microwave
infrared
visible light
ultraviolet
X-ray
gamma ray

 

 

Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps with 4 images

Blurred answer
Knowledge Booster
Atomic Structure and Spectra
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, chemistry and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Chemistry: An Atoms First Approach
Chemistry: An Atoms First Approach
Chemistry
ISBN:
9781305079243
Author:
Steven S. Zumdahl, Susan A. Zumdahl
Publisher:
Cengage Learning
Chemistry
Chemistry
Chemistry
ISBN:
9781133611097
Author:
Steven S. Zumdahl
Publisher:
Cengage Learning
Chemistry
Chemistry
Chemistry
ISBN:
9781305957404
Author:
Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Introductory Chemistry: A Foundation
Introductory Chemistry: A Foundation
Chemistry
ISBN:
9781337399425
Author:
Steven S. Zumdahl, Donald J. DeCoste
Publisher:
Cengage Learning
Chemistry for Engineering Students
Chemistry for Engineering Students
Chemistry
ISBN:
9781337398909
Author:
Lawrence S. Brown, Tom Holme
Publisher:
Cengage Learning
General Chemistry - Standalone book (MindTap Cour…
General Chemistry - Standalone book (MindTap Cour…
Chemistry
ISBN:
9781305580343
Author:
Steven D. Gammon, Ebbing, Darrell Ebbing, Steven D., Darrell; Gammon, Darrell Ebbing; Steven D. Gammon, Darrell D.; Gammon, Ebbing; Steven D. Gammon; Darrell
Publisher:
Cengage Learning