<P> In 1909, Hans Geiger and Ernest Marsden conducted experiments with thin sheets of gold . Their professor, Ernest Rutherford, expected to find results consistent with Thomson's atomic model . It wasn't until 1911 that Rutherford correctly interpreted the experiment's results which implied the presence of a very small nucleus of positive charge at the center of gold atoms . This led to the development of the Rutherford model of the atom . Immediately after Rutherford published his results, Antonius Van den Broek made the intuitive proposal that the atomic number of an atom is the total number of units of charge present in its nucleus . Henry Moseley's 1913 experiments (see Moseley's law) provided the necessary evidence to support Van den Broek's proposal . The effective nuclear charge was found to be consistent with the atomic number (Moseley found only one unit of charge difference). This work culminated in the solar - system - like (but quantum - limited) Bohr model of the atom in the same year, in which a nucleus containing an atomic number of positive charges is surrounded by an equal number of electrons in orbital shells . As Thomson's model guided Rutherford's experiments, Bohr's model guided Moseley's research . </P> <P> The plum pudding model with a single electron was used in part by the physicist Arthur Erich Haas in 1910 to estimate the numerical value of Planck's constant and the Bohr radius of hydrogen atoms . Haas' work estimated these values to within an order of magnitude and preceded the work of Niels Bohr by three years . Of note, the Bohr model itself only provides substantially - reasonable predictions for atomic and ionic systems having a single effective electron . </P> <P> A particularly useful mathematics problem related to the plum pudding model is the optimal distribution of equal point charges on a unit sphere called the Thomson problem . The Thomson problem is a natural consequence of the plum pudding model in the absence of its uniform positive background charge . </P> <P> The classical electrostatic treatment of electrons confined to spherical quantum dots is also similar to their treatment in the plum pudding model . In this classical problem, the quantum dot is modeled as a simple dielectric sphere (in place of a uniform, positively - charged sphere as in the plum pudding model) in which free, or excess, electrons reside . The electrostatic N - electron configurations are found to be exceptionally close to solutions found in the Thomson problem with electrons residing at the same radius within the dielectric sphere . Notably, the plotted distribution of geometry - dependent energetics has been shown to bear a remarkable resemblance to the distribution of anticipated electron orbitals in natural atoms as arranged on the periodic table of elements . Of great interest, solutions of the Thomson problem exhibit this corresponding energy distribution by comparing the energy of each N - electron solution with the energy of its neighbouring (N - 1) - electron solution with one charge at the origin . However, when treated within a dielectric sphere model, the features of the distribution are much more pronounced and provide greater fidelity with respect to electron orbital arrangements in real atoms . </P>

What was still missing in rutherford model of the atom