Preliminary Summary of the Bohr Atom

These three formulas can be used for quite a few applications which will be our introduction to spectroscopy. The most obvious application is to compare the energy formula to the experimental wavelengths of the H atom spectrum (Z= 1)  

This has the same type denominator as the Bahner formula and when the other numbers are compared, it is found that the Bohr equation is essentially the same as the Balmer equation. There is only a slight difference due to the fact that the nucleus in the Bohr model is fixed at die center of the atom while the real spectra include the fact that the electron and proton both orbit around the center-of-mass (the see-saw balance point) of the two particles. That is really very close to the position of the proton because it is much more massive than the electron. When this correction is made to the Bohr formula, the agreement with the experimental spectra is essentially exact. 

One other unit we may encounter in spectroscopy, particularly in infrared spectroscopy, is the wave number. Basically, the wave number is just the reciprocal of the wavelength  

This unit may have come about due to the way some early experiments were done to measure wavelengths and was important in the derivation of Rydberg s formula but it is now established in infrared spectroscopy. In particular, the combined Balmer-Rydberg formula in wave numbers is 

We can see that the Bohr s factor of constants should agree with the experimental value of the Rydberg. We have already noted there needs to be a small correction to the value of m since a tiny center-of-mass correction should be applied (the electron and proton actually rotate about then-mutual center of mass which is very close to the position of the more massive proton). 

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