Question

Although the Heisenberg uncertainty principle feels like merely a “negative” statement (we cannot reduce all uncertainties to zero), it can be used as a tool to make rough calculations. Consider an electron trapped in a box of size a= 0.5 ? (= .05 nm, the size of a hydrogen atom). Without doing any wave function calculations or assuming any particular well shape, use the uncertainty principle to estimate the smallest possible ?p. Assume that the particle’s momentum must be at least as big as the uncertainty in the momentum, thus giving you a lower bound for KE = p^2/2m. Do that to estimate the typical energy (find it in eV) of an electron trapped in an atomic-sized well. Does the energy scale (at least, the order of magnitude) seem reasonable?

          Although the Heisenberg uncertainty principle feels like merely a “negative” statement (we cannot reduce all uncertainties to zero), it can be used as a tool to make rough calculations. Consider an electron trapped in a box of size a= 0.5 ? (= .05 nm, the size of a hydrogen atom). Without doing any wave function calculations or assuming any particular well shape, use the uncertainty principle to estimate the smallest possible ?p. Assume that the particle’s momentum must be at least as big as the uncertainty in the momentum, thus giving you a lower bound for KE = p^2/2m. Do that to estimate the typical energy (find it in eV) of an electron trapped in an atomic-sized well. Does the energy scale (at least, the order of magnitude) seem reasonable?

Although the Heisenberg uncertainty principle feels like merely a “negative” statement (we cannot reduce all uncertainties to zero), it can be used as a tool to make rough calculations. Consider an electron trapped in a box of size a= 0.5 ? (= .05 nm, the size of a hydrogen atom). Without doing any wave function calculations or assuming any particular well shape, use the uncertainty principle to estimate the smallest possible ?p. Assume that the particle’s momentum must be at least as big as the uncertainty in the momentum, thus giving you a lower bound for KE = p^2/2m. Do that to estimate the typical energy (find it in eV) of an electron trapped in an atomic-sized well. Does the energy scale (at least, the order of magnitude) seem reasonable?

Added by Brandi L.

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