An early model for an atom considered it to have a positively charged point nucleus of charge $Z e$ , surrounded by a uniform density of negative charge upto a radius $R$ . The atom as a whole is neutral. The electric field at a distance $r$ from the nucleus is $(r < R)$

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An early model for an atom considered it to have a positively charged point nucleus of charge

Z e

, surrounded by a uniform density of negative charge upto a radius

R

. The atom as a whole is neutral. The electric field at a distance

r

from the nucleus is

(r < R)

An early model for an atom considered it to have a positively charged point nucleus of charge Z e , surrounded by a

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Correct answer: A. Ze 4 π _0 [(1)/(r^2)-(r)/(R^3)]

Charge on nucleus =+Z e Total negative charge =-Ze ( atom is electrically neutral) Negative charge density, = charge volume =(-Z e)/((4)/(3) π R^3) Consider a Gaussian surface with radius r . By Gauss's theorem, Charge enclosed by Gaussian surface, q=Z e+(4 π r^3)/(3) =Z e-Z e (r^3)/(R^3) (Using (i)) From (ii), E(r)=(q)/(4 π _0 r^2)= Z e-Z e (r^3)/(R^3) 4 π _0 r^2 =(Z e)/(4 π _0) [(1)/(r^2)-(r)/(R^3)]

An early model for an atom considered it to have a positively...

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