Question

A hydrogen atom is made up of a **proton** of
charge +*Q* = 1.60 x10^{-19} C and an
**electron** of charge –*Q*= –1.60 x
10^{-19} C. The proton may be regarded as a point charge at
the center of the atom. The motion of the electron causes its
charge to be "smeared out" into a spherical distribution around the
proton, so that the electron is equivalent to a charge per unit
volume of ρ ( r ) = − Q π a 0 3 e − 2 r a 0, where
*a*_{0} is called the Bohr radius = 5.29 x
10^{-11} m.

*a) Write down* (but do not solve!) the equation you
would use to find the value of the electric field inside the
hydrogen atom at some point a distance *r* from the
nucleus.

* So, get to the point right before
you would start actually evaluating the integral(s).*

b) Once you had the answer to part *a*, show how would
you find the potential at a radius *r* from the center of
the atom. (Again, don't evaluate any integrals)

Answer #1

Electric filed inside some point r can be calculated using gauss law which states

where q is total charge enclosed by gaussian surface which is at distance r for spherically symmetric distribution can be written as

So, from this equation you can calculate electric field at some point r.

b) at the center of atom let potential =0

so after evaluating electric field potential can be determine at point r as

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