The work done by the field of a nucleus in a complete circular orbit of the electron is

Zero

The correct answer is Option (4) - Zero

The nucleus exerts an electrostatic force on the orbiting electron. This force acts as the centripetal force and always point towards the centre of circular orbit -

$W=\vec F.\vec d=Fd\cos θ$

for a circular orbit, the force is always perpendicular to the instantaneous displacement of electron. 

$θ=90°$