To form a hydrogen atom, a proton is fixed at a point and an electron is brought from far away to a distance of 0.529 ✕ 10−10 m, the average distance between proton and electron in a hydrogen atom. how much work is done by the electric field (in j)?

1) First of all, let's calculate the potential difference between the initial point (infinite) and the final point (d=0.529x10-10 m) of the electron.
This is given by:

Where E is the electric field generated by the proton, which is
 
where  is the Coulomb constant and  is the proton charge.
Replacing the electric field formula inside the integral, we obtain


2) Then, we can calculate the work done by the electric field to move the electron (charge ) through this . The work is given by

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