Energy+Levels

=Energy Levels=

The energy levels of an atom can be determined using where //k// is the ionization energy of the atom, //Z// is the charge on the nucleus, and //n// is the principal quantum number--it is an integer >= 1 denoting the level in question. //n// = 1 is called the **//ground state//** of the atom, and //n// >= 2 are called **//excited states//**. For hydrogen, //Z// = +1 and //k// = 13.6 eV; the energy levels of the H atom are summarized in the table below for the first several values of //n//. As you can see, the energy levels get closer together as //n// increases; in other words, the difference between energies gets smaller. Practically, this means that an electron emitting a photon and dropping from //n// = 5 to //n// = 4 will release less energy (0.306 eV) than an electron dropping from //n =// 4 to //n// = 3 (0.66 eV); similarly, an electron in //n// = 3 will jump to //n// = 4 when it absorbs 0.66 eV and an electron in //n// = 4 will jump to //n// = 5 when it absorbs 0.306 eV.
 * = //**n**// ||= //**E**// (eV) ||
 * < 1 (ground state) ||= -13.6 ||
 * < 2 (1st excited state) ||= -3.4 ||
 * < 3 (2nd excited state) ||= -1.51 ||
 * < 4 (3rd excited state) ||= -0.85 ||
 * < 5 (4th excited state) ||= -0.54 ||

This has clear connections to atomic line spectra. Since there are discrete differences in energy levels, only photons of certain energies can be emitted. These are what appear in the emission line spectrum for that element; each element has different possible energy levels, and thus a particular spectrum. The converse is true for absorption spectra; only photons of certain energies can be absorbed to excite the atom, so dark lines of only certain wavelengths will appear in an otherwise continuous spectrum.

For the hydrogen atom, transitions to the ground state (//n// = 1) are called the //**Lyman series**//; these spectral lines occur in the ultraviolet region of the electromagnetic spectrum. Transitions to //n = 2// are called the **//Balmer series//**, and several of these appear in the visible range; they compose a prominent red, cyan, and dark blue set of spectral features. Transitions to //n// = 3 are called the //**Paschen series**//, while transitions to //n// = 4 are called the //**Brackett series**//; these lines all occur in the infrared.