Boron

When we go from beryllium to boron, we add a third electron to the E₂ energy level. From our experience with beryllium, we expect another significant increase in binding energy, up to perhaps 13 eV or 14 eV. But instead the binding energy drops from 9.32 eV down to 8.30 eV. Something broke the pattern and caused this drop.

At boron, both the E₂ , = 0 wave patterns are already full and the electron has to go into one of the E₂ , = 1 patterns. All the electron standing wave patterns with a non zero amount of angular momentum have a node at the origin. The more the angular momentum, the more spread out the node and the farther the electron is kept away from the nucleus. An electron in an  ≠ 0 wave pattern will thus be effectively screened by electrons in  = 0 wave patterns where the electron spends a lot of time right down at the nucleus. Thus we expect that electrons in  ≠ 0 patterns to be less tightly bound than those in the  = 0 pattern of the same energy level. This shows up with the drop in binding energy in going from beryllium to boron.

مواضيع ذات صلة

Linear systems

Confined waves, with natural frequencies

The reflection of waves

Einstein’s laws of radiation

The Boltzmann law

Energy levels

The size of an atom

Bremsstrahlung

Synchrotron radiation

Radiation damping

The rate of radiation of energy

Radiation resistance