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 a₀ 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