# Finding the bond length of hydrogen theoretically

If the bond length of two atoms is the distance where the force of repulsion is equal to the force of attraction, then one could figure out what the bond length of H2 is by setting the net force of attraction to the net force of repulsion and solving for distance. However when I try this ..... ((2.30976*10^-28)/( d ^2) )+ ((2.30976*10^-28)/(d+1.06*10^-10)^2)= ((-2.30976*10^-28 )/(d + 5.3*10^-11)^2) * 2........ Where d is the unknown distance between the two hydrogens valence electrons, 1.06*10^-10 is the distance of the two radii of each hydrogen ( because proton - proton repulsion has a distance of d and the length of the distance from the proton to it's valence electron times 2 because there are two protons repelling each other) 5.3*10^-11 is the radius of the hydrogen atom and 2.30976*10^-28 is the charge of the electron and proton ( the electron has a negative charge on it ) . The problem is that when I plug this in to an equation calculator, I don't get a real answer. I don't know where I went wrong,many help is appreciated, thanks.

## Answers and Replies

Just to clarify what I did, it's basically Coulomb's law for nuclear repulsion+ Coulomb's law for electron repulsion = Coulomb's law for electron - proton attraction ( I multiplied this by two because the proton of hydrogen 1 is attracted to the electron of hydrogen 2 and the electron of hydrogen 1 is attracted to the proton of hydrogen 2 so there are really two cases of attraction going on )