 #1
jerryfelix30
 2
 0
 Homework Statement:
 The effective charge density of the electron cloud in a hydrogen atom in its quantum mechanical ground state turns out to be given by pnot(e^(r/rnot)), where pnot is a negative constant (the clouds charge density at r=0) and rnot is a constant (rnot=0.025nm). Use gauss's law in integral form to calculate directly how E varies with r inside the electron cloud. Remember that there is a proton at r=0! Express your result in terms of the protons charge q.
 Relevant Equations:

Gauss's law= E dot dA=q(enclosed)/epsilon not
Q enclosed is the net charge enclosed in the shape and epsilonnot is the permittivity constant
Problem Statement: The effective charge density of the electron cloud in a hydrogen atom in its quantum mechanical ground state turns out to be given by pnot(e^(r/rnot)), where pnot is a negative constant (the clouds charge density at r=0) and rnot is a constant (rnot=0.025nm). Use gauss's law in integral form to calculate directly how E varies with r inside the electron cloud. Remember that there is a proton at r=0! Express your result in terms of the protons charge q.
Relevant Equations: Gauss's law= E dot dA=q(enclosed)/epsilon not
Q enclosed is the net charge enclosed in the shape and epsilonnot is the permittivity constant
The shape is a sphere so area is 4pi r^2
Ex4pir^2=q/epsilonnot
E=q/4pir^2(epsilonnot)
Relevant Equations: Gauss's law= E dot dA=q(enclosed)/epsilon not
Q enclosed is the net charge enclosed in the shape and epsilonnot is the permittivity constant
The shape is a sphere so area is 4pi r^2
Ex4pir^2=q/epsilonnot
E=q/4pir^2(epsilonnot)