PART A)
Electrostatic potential at the position of origin is given by
here we have
now we have
Now work done to move another charge from infinite to origin is given by
here we will have
so there is no work required to move an electron from infinite to origin
PART B)
Initial potential energy of electron
Now we know
now by energy conservation we will have
So here initial total energy is sufficient high to reach the origin
PART C)
It will reach the origin
Answer:
No, neutrons have about the same mass as a proton, but both have more mass than electrons.
Hope this helps a bit,
Flips