Quantum Mechanics is a purely mathematical description of the atom and the subatomic particles. But, that does not mean you have to be a nuclear physicist to understand how the atom is arranged or its importance. You can develop an appreciation and a basic understanding of the quantum atom by learning the major events that led to the discovery of the quantum atom.
# 1 Discovery of the Electron
In 1898 JJ Thomson proved the existence of the electron and changed our perception of matter forever. Although others (George Stoney) had predicted there were particles smaller than the atom, they were unable to prove it. JJ Thomson not only proved the existence of a subatomic particle; he proposed a new atomic model, the "Plum Pudding Model".
# 2 Discovery of the Nucleus and Proton
The discovery of the electron led others to test ideas that there might be other subatomic particles. One such person, a former student of JJ Thomson's, was Ernest Rutherford. Rutherford recruited two assistants, Hans Geiger and Ernest Marsden, to perform the now famous "Gold-foil Experiment". The result of this experiment led Rutherford to conclude that the atom must be mostly space with the majority of its mass located in a very small, dens, centrally located area of the atom. Rutherford named this dense, positively charged region the nucleus later determined that the positive charge was due to another subatomic particle he named the proton.
# 3 The Elements' Spectra
An early discovery, by Robert Bunsen and Gustav Kirchhoff, that was very important to the development of the Quantum Theory was the discovery of elemental spectra. It was discovered that each element had its own unique emission spectrum that could have been used like a fingerprint to identify the element. Later, the quantum theory would provide the explanation for the spectral lines.
# 4 The Quantum Theory
Max Planck developed an idea from the observation of black-body radiation that was originally based on a guess that electromagnetic energy could only be emitted in quantized amounts. In other words, the energy could only be used in whole number packages Planck called quanta. This idea became known as "Planck's Postulate" and historically wave birth to quantum mechanics.
# 5 The Photoelectric Effect
In 1905, Albert Einstein published four scientific papers that were to become his greatest works. One of these papers was his explanation of the photoelectric effect. The photoelectric effect is a phenomenon observed when electrons are emitted from matter exposed to beams of light with short wavelengths. In his explanation, Einstein suggested that light contained discrete quanta (photons) rather than continuous waves and the energy in these quanta caused light to have more like a particle, thus moving the electrons.
Probably the most important part of this discovery was Einstein's use of Planck's constant and Planck's equation in his explanation of the photoelectric effect. This action alone helped expand the quantum theory towards quantum mechanics.
# 6 Matter Waves
Probably one of the most astounding scientific discoveries was the de Broglie hypothesis. First proposed as part of Louis de Broglie's doctoral thesis, it stated that if light waves could possess properties then electrons should have wave properties. De Broglie had no empirical evidence whatsoever to support his idea, but based his hypothesis on the equations used by Einstein and Planck in their discoveries.
Matter waves were such a radical idea that de Broglie's advisors defered the thesis to Einstein who gave it high praise and agreed with wave-particle duality. Thus, de Broglie was granted his doctorate and a new form of physics was expanded.
# 7 The Uncertainity Principle
One of the most disputed topics in the early years of quantum physics was the Heisenberg uncertainty principle which stated that you can not know simultaneously both the position and the momentum of a particle with any certainty or accuracy.
Einstein, de Broglie and Planck would not accept the idea that it was impossible to know everything about a phenomenon. They believed that an equation exhausted that could tie everything together. But, none of them were able to produce it. However, Heisenberg, Born and Bohr were able to further their position in what is known as the Copenhagen Interpretation of quantum physics.