Maximal ionization of atoms

5 problems

• Atomic radius bounded independently of nuclear charge

  Open

  Heavy atoms are about the same size as light ones, roughly $10^{-8}$ cm across. Prove from the many-electron Schrodinger equation that the size of a neutral atom does not grow with Z.

• Excess electron number of atoms bounded independently of nuclear charge

  Open

  Show that there is one fixed number C such that no atom, however heavy, can bind more than Z + C electrons. Bind means the extra electrons stay attached instead of flying off to infinity.

• Uniform bound on the ionization energy of neutral atoms

  Open

  The energy needed to remove one electron from a neutral atom is a few eV for every element in the periodic table. Prove that it stays bounded as Z grows.

• Excess charge of molecules bounded by a constant per nucleus

  Open

  A molecule with several nuclei can also hold extra electrons. Show that the number of extra electrons is at most a fixed constant times the number of nuclei, whatever the nuclear charges and positions.

• No atom binds two extra electrons

  Open

  Experiments find no stable atom carrying two extra electrons. Prove from the Schrodinger equation that $N_c(Z) \le Z + 1$ for every element.