1175_Physics ProblemsTechnical Physics

1175_Physics ProblemsTechnical Physics - 516 Q42.6 Atomic...

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516 Atomic Physics Q42.6 From Equations 42.7, 42.8 and 42.9, we have −= = + =+ E ke r r r KU ee e e 22 2 . Then KE = and UE e =− 2. Q42.7 Bohr modeled the electron as moving in a perfect circle, with zero uncertainity in its radial coordinate. Then its radial velocity is always zero with zero uncertainty. Bohr’s theory violates the uncertainty principle by making the uncertainty product ∆∆ rp r be zero, less than the minimum allowable = 2 . Q42.8 Fundamentally, 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 . Q42.9 Bohr’s theory pictures the electron as moving in a flat circle like a classical particle described by Fm a = . Schrödinger’s theory pictures the electron as a cloud of probability amplitude in the three-dimensional space around the hydrogen nucleus, with its motion described by a wave equation. In the Bohr model, the ground-state angular momentum is 1
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