Exact, but not quite correct, solutions

The solutions we have described here are exact , in the mathematical sense that they can be obtained from the Schrodinger equation (eqn 4.17) without approximation. They are not quite correct , because this equation does not truly describe a real hydrogen atom. The errors are very small for hydrogen, but some of them become more significant in heavier atoms. They result from the following assumptions, none of which is quite correct  

only the electron moves, the nucleus being stationary  

Point 3, the assumption that Schriklinger s equation is exact, is very significant at a fundamental level. Einstein s Special Theory of Relativity proposed a modification of classical mechanics in a different direction from that of quantum mechanics. The corrections involved in Einstein s theory, which are not incorporated in Schrbdinger s equation, only become significant 

The first three lines in the spectrum of atomic hydrogen are found at the following wavenumbers  

Show that they fit eqn 4.11 with nt = 1, and n2 = 2, 3, and 4, respectively. Derive an accurate value for the Rydberg constant for hydrogen, and use it to calculate the ionization energy of hydrogen. Give your answer in electron volts and in kilojoules per mole. 

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