- #1
rokku
- 7
- 0
How does forming a bond between two ions lower the overall energy of the system? Also how would two hydrogen atoms form if there is proton-proton repulsion and electron-electron repulsion and only proton-electron attraction?
Pythagorean said:In the case of covalent bonding, it's a consequence of the indistinguishability of particles! Griffiths talks about this at the end of his Intro to Quantum book in Chapter 5. Essentially, the superposition that results from treating identical particles (they are treated as distinguishable classically) results in bosons (nucleus) being closer together and fermions (like electrons) being farther apart and once you consider spin, the electrons are able to occupy the "singlet" state where they are more likely to be in between the two nuclei, attracting them towards the center.
DrDu said:Indistinguishability is not the crucial point, given that you observe covalent bonding already for molecules containing only one electron, namely ##\mathrm{H}_2^+##.
Classically you won't expect a big effect, as nuclear-nuclear repulsion and electron-electron repulsion is made up at bonding distances by electron nuclear attraction.
In fact, covalent bonding is an essentially quantum mechanical effect. In the molecule, the electron can move in the potential throughs of two nuclei as compared to only one in the case of a single atom. This increases its positional uncertainty ##\Delta x## along the bond axis and by the uncertainty principle lowers its momentum uncertainty ##\Delta p=\hbar/\Delta x##.
Hence also its kinetic energy gets lower although the story doesn't end here.
There is an excellent article by Kutzelnigg, a quantum chemist, on the principle behind bonding:
http://onlinelibrary.wiley.com/doi/10.1002/anie.197305461/abstract
DrDu said:Indistinguishability is not the crucial point, given that you observe covalent bonding already for molecules containing only one electron, namely ##\mathrm{H}_2^+##.
Classically you won't expect a big effect, as nuclear-nuclear repulsion and electron-electron repulsion is made up at bonding distances by electron nuclear attraction.
In fact, covalent bonding is an essentially quantum mechanical effect. In the molecule, the electron can move in the potential throughs of two nuclei as compared to only one in the case of a single atom. This increases its positional uncertainty ##\Delta x## along the bond axis and by the uncertainty principle lowers its momentum uncertainty ##\Delta p=\hbar/\Delta x##.
Hence also its kinetic energy gets lower although the story doesn't end here.
There is an excellent article by Kutzelnigg, a quantum chemist, on the principle behind bonding:
http://onlinelibrary.wiley.com/doi/10.1002/anie.197305461/abstract
Pythagorean said:So the next claim Griffiths makes is that in the triplet state, the electron pair are "antibonding" which implies to me that they will prevent covalent bonding in that case. Is that true?
Ions bond together because of the attractive forces between positively and negatively charged particles. This attraction forms strong electrostatic bonds, which result in the formation of a stable compound.
The energy of two ions bonded together is lower than two ions separated because the bond formation releases energy. This energy is a result of the attractive forces between the ions, which reduces the potential energy of the system.
The energy of bonded ions is affected by the distance between the ions, the charge of the ions, and the size of the ions. A shorter distance, higher charge, and smaller ion size all contribute to a stronger bond with lower energy.
Yes, the energy of bonded ions can be broken down into different components such as electrostatic energy, kinetic energy, and potential energy. These components help to explain the overall energy of the bonded ions.
The bond strength between ions directly affects the overall energy of a compound. A stronger bond results in a lower overall energy, while a weaker bond leads to a higher energy. This is because stronger bonds require more energy to break, while weaker bonds require less energy.