Quantization of Energy

• Systems of particles in quantum mechanics are described by a mathematical function called a wavefunction. The wavefunction must fulfill various criteria. It must return a single value for each set of inputs; it must be continuous over its entire range; and the absolute square of the wavefunction must be integrable. Moreover, it must satisfy the time-dependent Schrodinger equation. The conditions imposed on the wavefunction imply that only certain wavefunctions are possible for a given system, each associated with a discrete value of energy. In other words, energy is quantized. You can't give an atom any amount of energy you choose; it can only have certain discrete values of energy.
  
  

Excited States

• The lowest-energy state of a quantum system is called the ground state, while higher-energy states are called excited states. Take hydrogen for an example. The wavefunctions of a hydrogen atom are called orbitals. A hydrogen atom in its ground state will have the electron in the lowest possible orbital, the 1s. If you gave the hydrogen atom additional energy -- if it absorbed a photon of electromagnetic radiation, for example -- the electron would "jump" to a higher orbital and the atom would now be in an excited state.
  
  

Emission

• Atoms emit energy in the form of electromagnetic radiation when they "decay" to a lower energy level, emitting a photon in the process. The atom can never have an energy of exactly zero. The energy of the photon it emits must equal the difference in energy between the excited state and the final state. This energy in turn corresponds to the frequency of the light it emits as dictated by Planck's equation, E = hv, where v is the frequency and h is a constant.
  
  

Spectra

• When atoms of a given element are heated, they emit light at certain characteristic wavelengths. These emission spectra are useful for physicists and astronomers; indeed, they were one of the clues that led to the development of quantum mechanics. It also follows that atoms can only absorb photons whose energies correspond to the difference between two allowed states. Consequently, the dark lines in an absorption spectrum for an element appear in the same places as the bright lines in an emission spectrum.