Quantum Mechanics
Photoelectric Effect
Albert Einstein demonstrated that the proportional relationship between the frequency of the incident light on a metal surface and the maximum kinetic energy of the electrons emitted from the metal can be explained if light energy is quantized in small bundles called photons. The energy of each photon is the product of its frequency and Planck's constant, or hf. A light beam consists of a beam of particles - photons - each having energy hf. The intensity (power per unit area) of a monochromatic light beam is the number of photons per unit area per unit of time, multiplied by the energy per photon. The interaction of the light beam with the metal surface consists of collisions between photons and electrons. During each of these collisions, the photon gives all its energy to an electron and the photon no longer exists. The electron is emitted from the surface after it receives the energy from a single photon. If the intensity of light is increased, more photons fall on the surface per unit time, and more electrons are emitted per unit time. However, each photon still has the same energy hf, so the energy absorbed by each electron is unchanged.

Atomic Spectra
When atoms of a single element in gaseous form are excited by an electric discharge and viewed throught a narrow-slit aperture,
hydrogen absorption spectrum:http://www.solarobserving.com/halpha.htm
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light is emitted from the atoms and seen as a discrete set of lines of different colors (wavelengths) that is characteristic of the element. The discrete lines did not agree with the classical electromagnetic theory that predicted that a charge oscillating with frequency f would radiate electromagnetic energy (light) of that frequency. Moreover, at that time the contemporary popular model of the atom was that the electrons of the atom were embedded in some kind of fluid that had most of the mass of the atom and enough positive charge to make the atom electrically neutral.

A set of experiments in which alpha particles (two protons and two neutrons, essentially a helium atom with no electrons) from radioactive radium were scattered by atoms in a gold foil showed that the number of alpha particles scattered at large angles could not be accounted for by an atom in which the positive charge was distributed throughout the atom (known to be about 0.1 nm in diameter). The results suggested that the positive charge and most of the mass of an atom is concentrated in a very small region (the nucleus), which has a diameter of about 0.00001 nm.

Stable Electron Orbits
The electron (e.g., of the hydrogen atom) moves in an orbit around the nucleus. Since there is an attractive charge between the positive nucleus and the negative electron, classical electromagnetic theory says that the atom will continuously radiate energy as the electron spirals into the nucleus. That does not happen because there are stable electron orbits, and the atom radiates energy only when the electron makes a transition from one stable orbit to another. This quantization of energy predicted by the quantum theory agrees with experiment. The atom absorbs or radiates an amount of light energy equal to the energy equivalent of the transition between orbits.

Chemical Properties
The quantum nature of electron orbitals and the energy associated with them is responsible for the reactivity of the elements and types of chemical bonds they form. In particular, the fact that hydrogen and carbon play such fundamental roles in living systems is a result of the quantum nature of their atomic structure.
Excerpted and adapted from:
1. Tipler, Paul A., and Gene Mosca. 2008. Physics for Scientists and Engineers. W. H. Freeman and Company, NY. 6th Edition