The plum pudding model is one of several historical scientific models of the atom. First proposed by J. J. Thomson in 1904 soon after the discovery of the electron, but before the discovery of the atomic nucleus, the model tried to explain two properties of atoms then known: that electrons are negatively-charged particles and that atoms have no net electric charge. The plum pudding model has electrons surrounded by a volume of positive charge, like negatively-charged "plums" embedded in a positively-charged "pudding". The word "plums" in 19th-century English "plum pudding" is an archaic use of the word; it referred at that time to raisins, not plums.
In this model, atoms were known to consist of negatively charged electrons. Though Thomson called them "corpuscles", they were more commonly called "electrons" which G. J. Stoney proposed as the "fundamental unit quantity of electricity" in 1891. At the time, atoms were known to have no net electric charge. To account for this, Thomson knew atoms must also have a source of positive charge to balance the negative charge of the electrons. He considered three plausible models that would be consistent with the properties of atoms then known:
Thomson chose the third possibility as the most likely structure of atoms. Thomson published his proposed model in the March 1904 edition of the Philosophical Magazine, the leading British science journal of the day. In Thomson's view:
... the atoms of the elements consist of a number of negatively electrified corpuscles enclosed in a sphere of uniform positive electrification, ...
With this model, Thomson abandoned his 1890 "nebular atom" hypothesis based on the vortex atomic theory in which atoms were composed of immaterial vortices and suggested that there were similarities between the arrangement of vortices and periodic regularity found among the chemical elements.:44–45 Being an astute and practical scientist, Thomson based his atomic model on known experimental evidence of the day. His proposal of a positive volume charge reflects the nature of his scientific approach to discovery which was to propose ideas to guide future experiments.
In this model, the orbits of the electrons were stable because when an electron moved away from the centre of the positively-charged sphere, it was subjected to a greater net positive inward force, because there was more positive charge inside its orbit (see Gauss's law). Electrons were free to rotate in rings which were further stabilized by interactions among the electrons, and spectroscopic measurements were meant to account for energy differences associated with different electron rings. Thomson attempted unsuccessfully to reshape his model to account for some of the major spectral lines experimentally known for several elements.
The plum pudding model usefully guided his student, Ernest Rutherford, to devise experiments to further explore the composition of atoms. Also, Thomson's model (along with a similar Saturnian ring model for atomic electrons put forward in 1904 by Nagaoka after James Clerk Maxwell's model of Saturn's rings) were useful predecessors of the more correct solar-system-like Bohr model of the atom.
The colloquial nickname "plum pudding" was soon attributed to Thomson's model as the distribution of electrons within its positively-charged region of space reminded many scientists of raisins, then called "plums," in the common English dessert, plum pudding.
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 was not 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.
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 provides reasonable predictions only for atomic and ionic systems with just one effective electron.
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.
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[clarification needed] with respect to electron orbital arrangements in real atoms.