516 Atomic PhysicsQ42.6From Equations 42.7, 42.8 and 42.9, we have −=−=+−=+EkerrrKUeeee222. Then KE=andUEe=−2.Q42.7Bohr modeled the electron as moving in a perfect circle, with zero uncertainity in its radialcoordinate. Then its radial velocity is always zero with zero uncertainty. Bohr’s theory violates theuncertainty principle by making the uncertainty product ∆∆rprbe zero, less than the minimumallowable =2.Q42.8Fundamentally, three quantum numbers describe an orbital wave function because we live in three-dimensional space. They arise mathematically from boundary conditions on the wave function,expressed as a product of a function of r, a function of θ, and a function of φ.Q42.9Bohr’s theory pictures the electron as moving in a flat circle like a classical particle described byFma∑=. Schrödinger’s theory pictures the electron as a cloud of probability amplitude in thethree-dimensional space around the hydrogen nucleus, with its motion described by a waveequation. In the Bohr model, the ground-state angular momentum is 1
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