In the center-of-mass reference frame of a hydrogen atom,
Chapter , Problem 27(choose chapter or problem)
In the center-of-mass reference frame of a hydrogen atom, the electron and nucleus have momenta that have equal magnitudes and opposite directions. (a) Using the Bohr model, show that the total kinetic energy of the electron and nucleus can be written where is called the reduced mass, is the mass of the electron, and M is the mass of the nucleus. (b) For the equations for the Bohr model of the atom, the motion of the nucleus can be taken into account by replacing the mass of the electron with the reduced mass. Use Equation 36-14 to calculate the Rydberg constant for a hydrogen atom that has a nucleus of mass Find the approximate value of the Rydberg constant by letting go to infinity in the reduced mass formula. To how many figures does this approximate value agree with the actual value? (c) Find the percentage correction for the ground-state energy of the hydrogen atom by using the reduced mass in Equation 36-16. Note: In general, the reduced mass for a two-body problem with masses and is given by
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