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(a) Show that the circular uncertainty principle can be written as ALAO> h/2, where AL is the uncertainty in angular momentum and AO is the uncertainty in angle. (b) How well can the angular position of the electron be specified in the Bohr atom?

(a) Show that the circular uncertainty principle can be written as ALAO> h/2, where AL is the uncertainty in angular momentum and AO is the uncertainty in angle. (b) How well can the angular position of the electron be specified in the Bohr atom?

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1. We can generalize the Heisenberg Uncertainty principle for position and momentum to in- clude circular motion. If As is the uncertainty in arc length and Ap, is the uncertainty in momentum tangent to the circle, then the circular uncertainty principle is ApsAs > ħ/2. (a) Show that the circular uncertainty principle can be written as ALAO > ħ/2, where AL is the uncertainty in angular momentum and A is the uncertainty in angle. (b) How well can the angular position of the electron be specified in the Bohr atom?
Transcribed Image Text:1. We can generalize the Heisenberg Uncertainty principle for position and momentum to in- clude circular motion. If As is the uncertainty in arc length and Ap, is the uncertainty in momentum tangent to the circle, then the circular uncertainty principle is ApsAs > ħ/2. (a) Show that the circular uncertainty principle can be written as ALAO > ħ/2, where AL is the uncertainty in angular momentum and A is the uncertainty in angle. (b) How well can the angular position of the electron be specified in the Bohr atom?
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