Dr. Richard F.W. BaderProfessor the ptcouncil.net / ptcouncil.net university / Hamilton,Ontario

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

TheNature of the Problem
2.TheNew Physics
3.The Hydrogen Atom
TheQuantization of Energy
TheProbability distribution of the Hydrogen Atom
AngularMomentum of an Electron in one 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 study of the hydrogen atom is more facility than our previousexample of an electron limit to move on a line. Not only does the motionof the electron take place in three dimensions however there is likewise a pressure actingon the electron. This force, the electrostatic pressure of attraction, isresponsible because that holding the atom together. The magnitude of this forceis given by the product of the nuclear and electronic charges separated bythe square of the distance between them. In the previous instance of anelectron confined to relocate on a line, the complete energy was completely kineticin origin because there to be no forces acting top top the electron. In the hydrogenatom however, the power of the electron, since of the force exertedon the by the nucleus, will certainly consist that a potential power (one i beg your pardon dependson the position of the electron family member to the nucleus) and a kineticenergy. The potential energy occurring from the pressure of attraction betweenthe nucleus and the electron is:
Let us imagine for the minute that the proton and the electron law classically.Then, if the nucleus is organized fixed in ~ the origin and the electron allowedto move relative come it, the potential power would vary in the manner indicatedin Fig. 3-1. The potentialenergy is independent of the direction in space and depends only on street r in between the electron and also the nucleus. Thus Fig.3-1 advert to any line directed from the nucleus to the electron.The r-axis in the figure may be taken literally as a line throughthe nucleus. Even if it is the electron moves to the right or to the left thepotential energy varies in the exact same manner.
Fig. 3-1.

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The potential power of interactionbetween a cell nucleus (at the origin) and an electron as a role of street r in between them.The potential power is zero as soon as the 2 particles are really far apart(r = ¥ ), and also equals minus infinitywhen r amounts to zero. Us shall take the energy for r = ¥as ours zero that energy. Every energy will it is in measured loved one to this value.When a secure atom is formed, the electron is attractive to the nucleus,ris less than infinity, and also the power will be negative. A negative valuefor the energy implies that energy must be gave to the mechanism if theelectron is to overcome the attractive pressure of the nucleus and escapefrom the atom. The electron has again "fallen into a potential well." However,the shape of the well is no much longer a straightforward square one as previously consideredfor one electron border to relocate on a line, but has the shape shown inFig.3-1. This form is a consequence of there gift a pressure actingon the electron and also hence a potential energy contribution i m sorry dependson the distance between the 2 particles. This is the nature that the problem.Now let united state see what quantum mechanics predicts because that the motion of the electronin such a situation.