Consider an oxygen (O₂) molecule in a bottle of air. Imagine that at a certain time, we locate the molecule along the x axis to within an uncertainty of 0.1 nm. (a) What is the minimum uncertainty in the molecule's x-velocity required by the Heisenberg Uncertainty Principle? (b) How does this compare (roughly) to the magnitude of the molecule's average x-velocity due to its thermal motion at room temperature? (Hints: Avogadro's number of oxygen molecules has a mass of about 32 g. At an absolute temperature T, a molecule has an average kinetic energy of kB T, where kB is Boltzmann's constant. Room temperature is about 295 K.)

Consider an oxygen (O₂) molecule in a bottle of air. Imagine that at a certain time, we locate the molecule along the x axis to within an uncertainty of 0.1 nm. (a) What is the minimum uncertainty in the molecule's x-velocity required by the Heisenberg Uncertainty Principle? (b) How does this compare (roughly) to the magnitude of the molecule's average x-velocity due to its thermal motion at room temperature? (Hints: Avogadro's number of oxygen molecules has a mass of about 32 g. At an absolute temperature T, a molecule has an average kinetic energy of kB T, where kB is Boltzmann's constant. Room temperature is about 295 K.)

University Physics Volume 3

17th Edition

ISBN:9781938168185

Author:William Moebs, Jeff Sanny

Publisher:William Moebs, Jeff Sanny

Chapter7: Quantum Mechanics

Section: Chapter Questions

Problem 38P: Suppose an electron is confined to a region of length 0.1 nm (of the order of the size of a hydrogen...

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