Black Body Radiation

On December 14, 1900, Max Karl Ernst Ludwig Planck (1858–1947) presented his quantum theory that was based on the results he obtained from experiments involving the black-body treated as an ensemble of harmonic oscillators. Quantum theory suggested matter can only emit radiation in equal portions called quanta. The energy of a quantum is proportionate to a single oscillator frequency within the black-body. The world famous Planck constant h = 6.62607 x 10−34 Js followed soon after the publication of the quantum theory. Quantification of energy eliminated the concept of ultraviolet catastrophe introduces through the work of Rayleigh and Jeans.

The Photoelectric Effect

In 1905, Albert Einstein tried to solve the problem of the photoelectric effect which suggested that light is able to knock electrons out of metals when their frequency exceeds defined thresholds. According to the classical theory, the energy of light should continuously be stored in metals regardless of its frequency, and after some time its energy should eject electrons from the metal. Experiments conducted to test this theory showed a completely different phenomenon that could not be explained through existing models. Einstein attempted to explain these newly observed phenomena through his idea of electromagnetic radiation quanta as particles. While Planck’s theory explained the movement of energy from the black-body to the electromagnetic field, Einstein’s theory looked at the energy transfer problem the other way around. Planck viewed quantum as a portion of energy and Einstein viewed it as a particle. The theory of photoelectric effect explained that energy transfers to electrons by quanta which is why only quanta exceeding some specific threshold (the binding energy of an electron in the metal) can eject electrons from metals. Einstein’s theory was later complemented by Gilbert Lewis’ explanations of photons and their nature.

Rutherford Model

In 1911, Ernest Rutherford a British physicist and acclaimed father of nuclear sciences proposed an experimental model of atoms. Rutherford introduced the idea that all atoms have a single nucleus that is much smaller in size than the size of the whole atom. Rutherford model stated that nuclei hold positive charges. While their approximate size equals only 10-13 centimetres, their density exceeds our imagination, as one cubic centimetre would weigh around three-hundred million tons. Rutherford’s theoretical research laid the foundations for understanding that every atom is made of a massive nucleus and electrons.

The Hydrogen Atom Model

At the beginning of the 20th century, atomic spectra, even of the simplest atoms such as hydrogen, were a great mystery to physicist trying to explain the nature of atoms. In 1913, 28-year-old Niels Bohr introduced his simple planetary model of atoms which was contrary to classical mechanics. According to this model, electrons did not fall on to the nucleus but changed their orbit instead, depending on the energy quanta they absorbed or emitted. Bohr theorised that the centrifugal force of electrons is compensated by the Coulomb attraction between the electron and the nucleus. He also suggested that the angular orbital momentum is quantized. This theory, however, was only able to explain the structure of hydrogen atom.

Bohr’s work inspired efforts to develop and popularize quantum mechanics among scientists, especially in the Copenhagen Institute for Theoretical Physics that Bohr founded in 1921. Hand- in-hand with Werner Heisenberg, Max Born, and John von Neumann, Bohr participated in explaining the basis of quantum mechanics. According to their view, quantum mechanics was a coherent and complete model of reality, and the discrepancies with classical mechanics had a profound and fundamental character.

The Old Quantum Theory

In 1916, Arnold Sommerfeld, a German theoretical physicist, tried to advance Bohr’s model and generalise the quantization rule to atoms containing more than one electron. Sommerfeld’s theory (or the old quantum theory) is not a coherent theory of general applicability. He assumed quantization for every periodic variable (such as an angle) could be described as an integral that equals an integer times the Planck constant.

Waves of Matter

In 1923, Louis de Broglie, a French physicist, introduced the concept of waves of matter - that both protons and any other particles have both wave properties and corpuscular characteristics -  or, in other words, particles are dual in their nature. De Broglie suggested that all matter can behave like waves and that the wavelength corresponds to momentum.  This theory, also known as de Broglie hypothesis, takes the central part in the theory of quantum mechanics. 


Cook, D. B. (2012). Quantum chemistry: a unified approach / David B. Cook. London: Imperial College Press; Singapore : Hackensack, NJ : Distributed by World Scientific Pub., 2012.

Levine, I. N. (2009). Quantum chemistry / Ira N. Levine. Upper Saddle River, N.J.: Pearson/Prentice Hall, c2009.

Neese, F. (2017). Quantum chemistry and EPR parameters. Blackwell Publishing Ltd. doi:10.1002/9780470034590.emrstm1505

Piela, L. (2013). Ideas of Quantum Chemistry. Amsterdam: Elsevier.

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