Demonstrate that the wavefunctions for the particle-on-a-ring problem show no preferred position on the ring, in other words that the probability of finding the particle at any particular angle, u'udd, is independent of the angular variable .

Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
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Chemistry
Question 6
Demonstrate that the wavefunctions for the particle-on-a-ring problem show no preferred position on the ring, in other words that the
probability of finding the particle at any particular angle, "dd, is independent of the angular variable .
Paragraph V B
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ON
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Question 12
An O₂ molecule confined in a nanoparticle to move along a one-dimensional path can be modeled as a particle in a box. If the path is 10
nm long, and our sample consists of a very large number of such systems, calculate the ratio of molecules that can be found in n-50,
relative to the number found in n-1. given that the ambient temperature is 77K.
Transcribed Image Text:Chemistry Question 6 Demonstrate that the wavefunctions for the particle-on-a-ring problem show no preferred position on the ring, in other words that the probability of finding the particle at any particular angle, "dd, is independent of the angular variable . Paragraph V B I UE E ON + v *** Question 12 An O₂ molecule confined in a nanoparticle to move along a one-dimensional path can be modeled as a particle in a box. If the path is 10 nm long, and our sample consists of a very large number of such systems, calculate the ratio of molecules that can be found in n-50, relative to the number found in n-1. given that the ambient temperature is 77K.
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