Chapter 39: Q6P (page 1215)
A proton is confined to a one-dimensional infinite potential well 100pm wide. What is its ground-state energy?
Short Answer
0.0205eV
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Chapter 39: Q6P (page 1215)
A proton is confined to a one-dimensional infinite potential well 100pm wide. What is its ground-state energy?
0.0205eV
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An electron is trapped in a one-dimensional infinite potential well. Show that the energy difference between its quantum levels n and n+2 is .
Light of wavelength 102.6 nm is emitted by a hydrogen atom. What are the (a) higher quantum number and (b) lower quantum number of the transition producing this emission? (c) What is the series that includes the transition?
As Fig. 39-8 suggests, the probability density for the region X>L in the finite potential well of Fig. 39-7 drops off exponentially according to , where C is a constant. (a) Show that the wave function that may be found from this equation is a solution of Schrödinger’s equation in its one-dimensional form. (b) Find an expression for k for this to be true.
From the energy-level diagram for hydrogen, explain the observation that the frequency of the second Lyman-series line is the sum of the frequencies of the first Lyman-series line and the first Balmer-series line. This is an example of the empirically discovered Ritz combination principle. Use the diagram to find some other valid combinations.
A muon of charge -eand mass(whereis the mass of an electron) orbits the nucleus of a singly ionized helium atom (He+). Assuming that the Bohr model of the hydrogen atom can be applied to this muon–helium system, verify that the energy levels of the system are given by
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