Abstract
A three dimensional representation of the probability density of a hydrogen 1s orbital in a spherical glass block was developed. It was compared with a two dimensional hydrogen atomic orbit proposed by E. Rutherford. In 1897, J. J. Thomson discovered the electron. The atomic nucleus was discovered by E. Rutherford in 1911. These epoch-making findings in the history of chemistry and physics lead to an atomic orbit model as a planet around the sun (Figure 1(a)). This orbit model had a problem in that the line spectrum (Figure 2 (b)) emitted from excited hydrogen atoms could not be explained. N. Bohr solved the problem assuming that the energies of the electron in a hydrogen atom are quantized, but the atomic orbit model was incorrect because it was based on classical mechanics. In 1924, L. de Broglie proposed that all moving particles such as electrons exhibit wave behavior. E. Schrödinger's equation, published in 1926, describes an electron as a wavefunction. Although this concept was mathematically convenient, it was difficult to visualize. M. Born proposed that Schrödinger's wavefunction could be used to calculate the probability of finding an electron at any given location around the nucleus. A three dimensional representation of Born's probability density of a hydrogen 1s orbital in a spherical glass block was developed (Figure 1(b)). This model allows that the electron may exhibit the properties of both a wave and a particle. The concept of "electron cloud" is frequently used, however, it leads to misunderstanding about an electron, because the observation of an electron gave always a point image of a particle, as was shown on the experiment of the interference of the electron beam using a biprism. The two slit interference experiment with electrons was performed by A. Tonomura [9]. The wave-particle duality of electrons was demonstrated in this experiment using an electron microscope equipped with an electron biprism and a position sensitive electron-counting system. Electrons incident on a wall with two slits pass through the slits and are detected one by one on a screen behind them. The electron is detected as a particle at a point somewhere on the screen according to the probability distribution of the interference pattern (Figure 3). In Figure 1(b), an electron can potentially be found at any distance from the nucleus, but, depending on the square of hydrogen 1s wavefunction, exists more frequently in certain regions around the nucleus than others.
