Modern Physics
Modern Physics
2nd Edition
ISBN: 9780805303087
Author: Randy Harris
Publisher: Addison Wesley
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Chapter 6, Problem 13E
To determine

To Show: ψ(x)=A'eikx+B'eikx is equivalent to ψ(x)=Asin(kx)+Bcos(kx) .

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Prove that, to three-digit accuracy, h = 4.14×10−15 eV ⋅ s, as stated in the text.
Consider the electron in a hydrogen atom is in a state of ψ(r) = (x + y + 3z)f(r).where f(r) is an unknown function depending only on r.(a) Is ψ an eigenstate of Lˆ2? Find the eigenvalue if your answer is ’Yes’.(b) Compute the probabilities of finding this electron in eigen states with m = −1, 0, +1. (c) Compute <Lz> in this state.
In class, we derived the formula for the power radiated by an accelerating charge. The classical model of the Hydrogen atom treats the electron as a point charge moving in a circular orbit about the inertial proton. In its ground state, the kinetic energy of this electron is 13.6 eV, and it’s radius is equal to the Bohr radius a0 = 0.0529 nm. If this electron behaves classically, what fraction of its energy does it radiate per orbit? Per second?
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