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Coulomb's Law - Mathematical Form

An early mode...

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An early model for an atom considered it to have a positively charged point nucleus of charge Ze, surrounded by a uniform density of negertive charge up to a radius R. The atom as a whole is neutral. For this model, what is the eletric field at a distance r from the nucleus?

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Q. 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)

.

Q. An atom is modelled as a point charge of +e at the nucleus with the electron charge distribution, described by the charge density

ρ = \frac{- 15 e}{8 π a^{3}} (1 - \frac{r^{2}}{a^{2}})

r \leq a < 0

ρ ≃ 0

r > a,

where 'a' is a constant.

The net charge contained within a sphere of radius r < a is :

Q. The nuclear charge

(Z e)

is non-uniformly distributed within a nucleus of radius

R

. The charge density

ρ (r)

( charge per unit volume) is dependent only on the radial distance

r

from the centre of the nucleus as shown in figure. The electric field is only along the radial direction. The electric field within the nucleus is generally observed to be linearly dependent on

r

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