Minimum finite distance in Di-hydrogen

[dlesswater]

A simplest example of a chemical bond is that formed by two hydrogen atoms in a H2 molecule.

a) Show that in the ground state (both electrons in the bonding orbital), the molecular energy has a minimum at a finite distance r=.074nm, defining the bond length for H2.
b) Determine the energy needed to break this bond.


I know we need to use the Coulomb force E(R)=e^2/R and the overall interaction E(R)=E-Ae^(-R/a)



The idea I believe is to combine these 2 equations to get the total energy in this system and then solve for R? Is that correct, and if so can you help explain to me why we can do this or why these 2 equations.I am not sure how to approach part B.

 

[NateD]

Yes, the idea is to combine these two equations to get the total energy in this system and then solve for R. We use the Coulomb force equation because it describes the interaction between two particles with opposite charges (in this case, two protons). The overall interaction equation describes the repulsive force between particles as they get closer together, which is represented by the exponential term. The energy needed to break the bond is equal to the energy difference between the bond length and infinity. This is because the bond length represents the point at which the total energy is at its lowest. To calculate this, we can integrate the total energy equation from R=infinity to R=the bond length to get the energy needed to break the bond.