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 nanometers. a) What is the minimum uncertainty in the molecule's x-velocity required by the Heisenberg Uncertainty Principle? (Hint: the answer is about 10 m/s) b) How does this compare (roughly) to the magnitude of the molecule's average x-velocity due to its thermal motion at room temperature? (Hint: the answer is delta v << average thermal speed) (Hint: Avogadro's number of oxygen molecules has a mass of about 32 grams. At an absolute temperature T, a molecule has an average kinetic energy of 1.5 * 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 nanometers.
a) What is the minimum uncertainty in the molecule's x-velocity required by the Heisenberg Uncertainty Principle? (Hint: the answer is about 10 m/s)
b) How does this compare (roughly) to the magnitude of the molecule's average x-velocity due to its thermal motion at room temperature? (Hint: the answer is delta v << average thermal speed)
(Hint:
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