The Quantum-Mechanical Atom
Schrodinger’s equation is analytically solvable for the H atom
Schrodinger’s equation cannot be solved analytically for atoms with more than one electron
Very complicated standing waves, hard to visalize
no classical electron orbits, replaced by probability clouds...
discrete energy spectra, characterized by three quantum numbers
- n: associated with the electrons energy (n=1,2,3,4…..)
- l : associated the angular momentum’s magnitude (l=0,1,2…n-1)
- ml : characterizing the direction of the angular momenta (it’s projection on a given direction) (ml=-l, -l+1, -l+2, ….l-1,l)
an additional quantum number: ms not explained by the classical theory of Schrodinger
ms characterizes the spin of the electron
- two possible orientations: up and down (dependent on the spinning direction)
four quantum number label the possible states of the electrons in atoms