R=1/2m2Ze(h/2x)2 The Bohr formula for energy levels did not agree as well with the observed pattern of emission spectra for species containing more than a single electron. However, it does give a reasonable fit, for example, to the Na atom spectra if one examines only transitions involving only the single valence electron. The primary reason for the breakdown of the Bohr formula is the neglect of electron-electron Coulomb repulsions in its derivation Nevertheless, the success of this model made it clear that discrete emission spectra could only be explained by introducing the concept that not all orbits were allowed". Only special orbits that obeyed a constructive- interference condition were really accessible to the electrons motions. This idea that not all energies were allowed, but only certain quantized"energies could occur was essential to achieving even a qualitative sense of agreement with the experimental fact that emission spectra were discrete In summary, two experimental observations on the behavior of electrons that were crucial to the abandonment of newtonian dynamics were the observations of electron diffraction and of discrete emission spectra. Both of these findings seem to suggest that electrons have some wave characteristics and that these waves have only certain allowed (i.e, quantized) wavelength So, now we have some idea about why Newton s equations fail to account for the dynamical motions of light and small particles such as electrons and nuclei. We see that extra conditions(e.g, the Bragg condition or constraints on the de broglie wavelength) could be imposed to achieve some degree of agreement with experimental observation10 R = 1/2 me Z2 e4 /(h/2p) 2 . The Bohr formula for energy levels did not agree as well with the observed pattern of emission spectra for species containing more than a single electron. However, it does give a reasonable fit, for example, to the Na atom spectra if one examines only transitions involving only the single valence electron. The primary reason for the breakdown of the Bohr formula is the neglect of electron-electron Coulomb repulsions in its derivation. Nevertheless, the success of this model made it clear that discrete emission spectra could only be explained by introducing the concept that not all orbits were “allowed”. Only special orbits that obeyed a constructive-interference condition were really accessible to the electron’s motions. This idea that not all energies were allowed, but only certain “quantized” energies could occur was essential to achieving even a qualitative sense of agreement with the experimental fact that emission spectra were discrete. In summary, two experimental observations on the behavior of electrons that were crucial to the abandonment of Newtonian dynamics were the observations of electron diffraction and of discrete emission spectra. Both of these findings seem to suggest that electrons have some wave characteristics and that these waves have only certain allowed (i.e., quantized) wavelengths. So, now we have some idea about why Newton’s equations fail to account for the dynamical motions of light and small particles such as electrons and nuclei. We see that extra conditions (e.g., the Bragg condition or constraints on the de Broglie wavelength) could be imposed to achieve some degree of agreement with experimental observation