What if atoms obeyed an inverse-cubed law

[bobsmith76]

atoms would be impossible in a universe ruled by an inverse-cube law because there would be no stable orbits for electrons.

The above sentence comes from Rees' book Just Six Numbers. I don't get it. Why would an inverse-cube law affect the stability of electron orbits?

 

[Bill_K]

Because for an inverse-cube potential, there is no ground state!

 

[Snip3r]

they will obey inverse cube law if universe had 4 space dimensions

 

[maverick_starstrider]

Because for an inverse-cube potential, there is no ground state!

Not to mention flux is no longer conserved. That's a special property of 1/r^2 laws that we often take for granted.