A hydrogen nucleus has a radius of 1 x 10-15 m and the electron is about 5.3 x 10-11 m from the nucleus. Assume the hydrogen atom is a ball with a radius of about 5.3 x 10-11 m and the nucleus is a ball with a radius of 1 x 10-15 m. How much work (in electron volts) must be performed by an external force to bring in another proton (from very far away) to the "surface" of the nucleus?

Answer 1

Until you get to the electron, no work needs to be done because there is no net charge on the atom.

From the electron ball (R1 radius) in to the proton ball (R2 radius), there is a repulsive force of
F = k/r^2 form

(I am leaving the Coulomb law numbers for you to do)

the work done in going from radius R1 to radius R2 is

integral from R1 to R2 of k dr /r^2
which is -(k/R1 -K/R2)

note that because R2 is less than R1, the quantity inside the parentheses is negative and therefore the work done is positive)