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Anearly model for an atom consider it to have a positively charged point inucleus ofcharges ze surronded by awhole is neutral for this model what is the electric fieldat a distance r from the nucleus |
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Answer» Solution :The charge distributionfor this model of the atom is asthe total chargein the uniform sperical of charge z e + NEGATIVE harge is neutral this immedialtely gives us the negative charge density p since we MUST have `(4piR^(3))/(3) p= 0-Ze` to fin d the electricfieldE(r ) at apointP whichis a distance r awayfrom the nucleuswe usegausslawits direction is alongtheradius vector rfrom the origin to the pointthe OBVIOUS gaussian surface is a spherical surface centredto the point P the obviousgaussian surfaceis a spherical surfacecentred at the nucleus we CONSIDER twosituation namely `rgtR` and `rlt R` (i) `r gt R`the electricflux `Phi`enclosedbythe spherical surface is `Phi =E(r )xx4 pi r^(2)` where E(r )is the magnitude of the electricfieldat r this is because the FIELD at any pointon the sphericaland has the same magnitude at all points on the surface i.e `q=Ze+(4pir^(3))/(3) P` substituting for the charge density p obtained earlier we haveM (ii)`r gt R`in this case the totalenclosed by the gaussiansperical surface is zerosince the atom is neutral thus from gauss law at r =R both cases given the same result E =0 |
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