Dr. Richard F.W. BaderProfessor the thedailysplash.tv / thedailysplash.tv university / Hamilton,Ontario

You are watching: What force of attraction holds the electron in the hydrogen atom

TheNature that the Problem
2.TheNew Physics
3.The Hydrogen Atom
TheQuantization that Energy
TheProbability distribution of the Hydrogen Atom
AngularMomentum of one Electron in an H Atom
SomeUseful Expressions
5.ElectronicBasis because that the nature of the Elements
6.TheChemical Bond
7.Ionicand Covalent Binding
Tableof contour Values
The Hydrogen AtomThe examine of the hydrogen atom is more complex than our previousexample of one electron border to move on a line. Not just does the motionof the electron take place in three dimensions however there is also a force actingon the electron. This force, the electrostatic force of attraction, isresponsible for holding the atom together. The size of this forceis offered by the product of the nuclear and electronic charges separated bythe square of the distance in between them. In the previous example of anelectron limit to relocate on a line, the complete energy was completely kineticin origin due to the fact that there were no pressures acting top top the electron. In the hydrogenatom however, the power of the electron, because of the pressure exertedon the by the nucleus, will certainly consist of a potential energy (one i m sorry dependson the place of the electron loved one to the nucleus) as well as a kineticenergy. The potential energy occurring from the force of attraction betweenthe nucleus and the electron is:
Let united state imagine because that the moment that the proton and the electron law classically.Then, if the cell nucleus is organized fixed in ~ the origin and the electron allowedto move relative to it, the potential power would vary in the way indicatedin Fig. 3-1. The potentialenergy is live independence of the direction in an are and depends only on street r between the electron and also the nucleus. Therefore Fig.3-1 advert to any kind of line directed from the nucleus come the electron.The r-axis in the figure may it is in taken literally together a line throughthe nucleus. Even if it is the electron move to the best or come the left thepotential energy varies in the very same manner.
Fig. 3-1.

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The potential energy of interactionbetween a nucleus (at the origin) and an electron as a role of street r between them.The potential power is zero when the 2 particles are really far apart(r = ¥ ), and also equals minus infinitywhen r equates to zero. We shall take it the power for r = ¥as ours zero that energy. Every power will be measured relative to this value.When a stable atom is formed, the electron is attractive to the nucleus,ris less than infinity, and the power will it is in negative. A negative valuefor the power implies that power must be offered to the mechanism if theelectron is to conquer the attractive force of the nucleus and escapefrom the atom. The electron has again "fallen right into a potential well." However,the shape of the fine is no longer a straightforward square one as previously consideredfor one electron border to move on a line, yet has the shape shown inFig.3-1. This form is a repercussion of there gift a pressure actingon the electron and also hence a potential energy contribution which dependson the distance between the 2 particles. This is the nature that the problem.Now let united state see what quantum mechanics predicts for the activity of the electronin such a situation.