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Coulomb's Law - Mathematical Form

an early mide...

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an early midel for an atom considered it ti have a positively charged point nucleus of charge Ze, surrounded by a uniform density of negative charge upto a radius R.the atom as a whole is neutral. for this model,what is electric field at a dis†an ce 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. A muonic atom contains a nucleus of charge Ze and a negative muon,

μ^{-}

, moving about it. The

μ^{-}

is an elementary charge with -e and a mass that is approximately 200 times as large as an electron mass.

What is the wavelength of the first line(

in \circ A

) in the Lyman series for such an atom?

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