Question

An early model for an atom considered it to have a positively charged point nucleus of charge Ze,surrounded by a uniform density of negative charge up to a radius R.The atom as a whole is neutral.For this model what is the electric field at a distance r from the nucleus.Can u expalin this answer in a different way other then the one given in the textbook.

Answer 1

Lets try to understand this from the very basic. According the Thomson model of the atom, the Electric field in an atom is experienced only up to the distance, which is less than the atomic radius.

Now, electric field at a distance 'r ' from the nucleus is 

E=kZe/r2

for (r>=R) where R is the Atomic Radius

Therefore, E=0 

Answer 2

Final Answer :
When r <=R, E(r) = 0
When r >R, E(r) = Ze/4π£° (1/r^2 - r/R^3)

STEPS AND Understanding :
1) We know, that size of Nucleus in negligible as compared to Nucleus.
So, At any distance r, we have to understand there exists nucleus with charge( +Ze. )

2) As atom is Neutral, the total Negative Charge in a sphere of Radius R is (-Ze. )


3) We will find Negative charge density to calculate charge at any distance r.

4) We will. apply Gauss law to find Electric Field at less than equal to R distance and more than that.


For Calculation see pic