Effective principal quantum number

The effective (main) quantum number (also or ) is required in quantum physics in order to take into account the shielding of the outer electron shells from the positively charged atomic nucleus by the inner electron shells. For example, with lithium as the lightest element with two electron shells, the inner 1s shell shields the 2s shell located further out from the core. ${\displaystyle n_{\text{eff}}}$ ${\displaystyle n'}$ ${\displaystyle n^{*}}$

use

The effective quantum number of an electron shell is defined as

${\displaystyle n_{\text{eff}}=n-\delta _{n,l}\!\,}$

With

• the respective principal quantum number and ${\displaystyle n}$
• the quantum defect , which in turn depends on the principal quantum number and mainly the orbital angular momentum . ${\displaystyle \delta }$ ${\displaystyle l}$

Replace the formula for the binding or ionization energy of the electrons of the hydrogen-like alkali atoms ${\displaystyle E_{n}}$

${\displaystyle E_{n}=-{\frac {Z^{2}}{n^{2}}}\mathrm {Ry} }$

With

• the atomic number ${\displaystyle Z}$
• the Rydberg energy  = 13.59843340  eV for hydrogen ${\displaystyle \mathrm {Ry} }$

the principal quantum number by the effective quantum number:

${\displaystyle E_{n,l}=-{\frac {Z^{2}}{n_{\text{eff}}^{2}}}\mathrm {Ry} ,}$

this adapted formula can also be used to describe shielded states, i.e. H. Atoms or ions with more than one electron.

swell

• Wolfgang Demtröder: Experimental Physics 3: Atoms, Molecules and Solids . Springer, Berlin, Heidelberg 2009, ISBN 978-3-540-68210-3 .