The quantum mechanical particle-in-a-box experiment- A revisit using NMR spectroscopy.

14 September 2023, Version 1
This content is a preprint and has not undergone peer review at the time of posting.


The particle-in-a-box experiment is a well-known method used to teach quantum mechanics concepts in physical chemistry labs for undergraduates. The investigation involves measuring the wavelength at maximum absorbance (max) of electronic transitions in the UV-vis spectrum and linking it to the box length. As the electronic configurations directly influence the nuclear shielding, a computational approach to estimate the nuclear magnetic resonance (NMR) chemical shifts is shown to relate to the box length. This article revisits what Flewwelling and Laidlaw suggested over 50 years ago: NMR chemical shifts can indirectly relate to the box's length via electron density calculations. For a series of molecules (polyenylic ions) of increasing carbon chain length, the activity allows the students to develop a broader understanding of how Schrödinger's equation for a particle in a box model, electron density calculations, and NMR spectroscopy are all connected at the atomic level. Additionally, the open-ended computational procedure leverages easily accessible tools to estimate NMR chemical shifts, and this approach is suitable as a viable remote learning exercise that supplements traditional UV-vis experiments.


Upper-division undergraduate
Physical Chemistry
Computer-Based Learning
Remote learning
quantum mechanics
NMR Spectroscopy.


Comments are not moderated before they are posted, but they can be removed by the site moderators if they are found to be in contravention of our Commenting Policy [opens in a new tab] - please read this policy before you post. Comments should be used for scholarly discussion of the content in question. You can find more information about how to use the commenting feature here [opens in a new tab] .
This site is protected by reCAPTCHA and the Google Privacy Policy [opens in a new tab] and Terms of Service [opens in a new tab] apply.