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The total wavefunction of an atom is approximated as the sum of the wavefunctions of the individual atomic orbitals. This is only an approximation as it takes an average value of the electron-electron interactions between electrons in the different orbitals.
In a hydrogenic (one electron) species, the frequencies of the lines in the atomic absorption or emission spectra corresponds to transitions between different energy levels.
The interaction between the spin angular momentum quantum numbers of two electrons gives rise to states of so called different spin multiplicity, such as singlet and doublet states.
If we consider the first ionization energy of lithium, we find that its value, at 5.39 eV, would have to result from an effective nuclear charge of 0.63. This implies that there is a higher degree of screening than can be explained, as perfect screening would result in a Zeff value of one. In fact, the ground stateelectronic configuration of lithium is 1s22s1, and the least tightly bound electron is in the 2s orbital, where Zeff = 1.26.
This repulsion between electrons in many electron species which opposes the attraction of the electrons towards the nucleus, and which causes the energies of the atomic orbitals in many electron species to be lower in the hydrogenic species is known as electron shielding.
In the description of the energies of transition of the hydrogen atom, the n values for the different energies are known as the principal quantum number for that energy level.
The wavefunction for a given atomic orbital has a characteristic mathematical expression.
When an atom has more than one electron, the electronic structure of the atom cannot be simply described as the electron-electron repulsion makes solving Schrodinger’s equation very hard. Instead, an approximation is made that the wavefunction of a two electron atom or ion is obtained by assigning each electron to one of the atomic orbitals of hydrogen. This is known as the orbital approximation.
Most atoms are made up of a nucleus surrounded by Z electrons, where Z, the atomic number, is the charge on the nucleus. The forces in these many-electron atoms include the electrostatic attraction between the electrons and the nucleus, but also electrostatic repulsion between the electrons.