Editing Energy level (section)

==== Orbital state energy level: atom/ion with nucleus + one electron ====
Assume there is one electron in a given atomic orbital in a [[Hydrogen-like atom|hydrogen-like atom (ion)]]. The energy of its state is mainly determined by the electrostatic interaction of the (negative) electron with the (positive) nucleus. The energy levels of an electron around a nucleus are given by: 
: <math>E_n = - h c R_{\infty} \frac{Z^2}{n^2}</math>
(typically between 1&nbsp;[[electronvolt|eV]] and 10<sup>3</sup>&nbsp;eV), where {{math|''R''<sub>∞</sub>}} is the [[Rydberg constant]], {{mvar|Z}} is the [[atomic number]], {{mvar|n}} is the principal quantum number, {{math|''h''}} is the [[Planck constant]], and {{math|''c''}} is the [[speed of light]]. For hydrogen-like atoms (ions) only, the Rydberg levels depend only on the principal quantum number {{mvar|n}}.

This equation is obtained from combining the [[Rydberg formula#Rydberg formula for any hydrogen-like element|Rydberg formula for any hydrogen-like element]] (shown below) with {{math|1=''E'' = ''h&nu;'' = ''hc'' / ''&lambda;''}} assuming that the principal quantum number {{mvar|n}} above = {{math|''n''<sub>1</sub>}} in the Rydberg formula and {{math|1=''n''<sub>2</sub> = ∞}} (principal quantum number of the energy level the electron descends from, when emitting a [[photon]]). The [[Rydberg formula]] was derived from empirical [[Emission spectrum|spectroscopic emission]] data.
: <math>\frac{1}{\lambda} = RZ^2 \left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)</math>

An equivalent formula can be derived quantum mechanically from the time-independent [[Schrödinger equation]] with a kinetic energy [[Hamiltonian operator]] using a [[wave function]] as an [[eigenfunction]] to obtain the energy levels as [[Eigenvalue#Schrödinger equation|eigenvalues]], but the Rydberg constant would be replaced by other fundamental physics constants.