How are the energy levels calculated

Helium energy levels

In the ground state of helium there are two identical 1s electrons. The energy required to remove one of these electrons is the highest ionization energy of all elements in the periodic table: 24.6 electron volts. The energy to remove the second electron is 54.4 eV - as expected when calculated from hydrogen energy levels. The He + ion is like a hydrogen atom, only with two charges in the core. Since the hydrogen energy levels depend on the square of the nuclear charge, the energy of the electron in helium should be 4 x (-13.6 eV) = 54.4 eV - and that is exactly what is observed.

The fact that the second electron is less strongly bound can be seen as a shielding effect: one electron partially shields the charge of the nucleus from the other electron. The shielding effect can be calculated with the energy:

One can also look at the energy from the point of view that the repulsion of the electrons represents a positive potential energy, which slightly increases the negative energy potential of the attractive electrical force of the nucleus. The description of any electron in a multi-electron atom must take into account the influence of the other electrons on the energy.

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