Assume that the proton is a uniformly charged sphere of radius R. (a) Show for the...

  

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Assume that the proton is a uniformly charged sphere of radius R. (a) Show for the hydrogen atom that the potential energy of the electron in the field of the proton is given by 3e2 R2 2R3 (-) V (r) = e2 Hint: Use Gauss's law and remember that the potential energy V (r) must be continuous. (b) Calculate the energy shift for the Is and 2p states of hydrogen if the potential energy in (a) is used. What effect does this shift have upon the Lyman a wavelength? Suggestion: You can use the fact that R ao to simplify the integrand before evaluating the integrals. Assume that the proton is a uniformly charged sphere of radius R. (a) Show for the hydrogen atom that the potential energy of the electron in the field of the proton is given by 3e2 R2 2R3 (-) V (r) = e2 Hint: Use Gauss's law and remember that the potential energy V (r) must be continuous. (b) Calculate the energy shift for the Is and 2p states of hydrogen if the potential energy in (a) is used. What effect does this shift have upon the Lyman a wavelength? Suggestion: You can use the fact that R ao to simplify the integrand before evaluating the integrals.