An early model of the atom, proposed by Rutherford after his discovery of the at

Question

An early model of the atom, proposed by Rutherford after his discovery of the atomic nucleus, had a positive point charge, +Ze (the nucleus) at the center of a sphere of radius R with uniformly distributed negative charge -Ze. Z is the atomic number, the number of protons in the nucleus and the number of electrons in the negative sphere. (18 = 7+4+7) (a) Show that the electric field inside the atom is E = (Ze)/((4pi)(epsilon)) ((1/r^2) - (r)/(R^2)) (b) What is the electric field at the surface of the atom? Is this the expected value? Explain (c) A uranium atom has Z= 92 and R= 0.10nm. What is the electric field at r= R/2?

Explanation / Answer

electric field due to proton is kZe/r^2

electric field due to uniformly distributed charge=-kZer/R^3

total=(Ze)/((4pi)(epsilon)) ((1/r^2) - (r)/(R^2))

b)electric field at surface =zero

c)electric fild for Z=92 and R=0.1nm

92*9*10^9*1.6*10^-19(1/(0.5*0.1*10^-10)^2-0.5/(0.1*10^-10))=5.3*10^15N/C

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