Why will chlorine atom attract electron.

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Homework Statement


Suppose that there is an isolated chlorine atom and there is an isolated electron in its surroundings. Then what force will act on the electron to pull it towards the atom.



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The Attempt at a Solution



I know that chlorine will attract the electron but I am unable to identify what force will be acting on the electron to pull it towards the chlorine atom. I think that as the chlorine atom is neutral there will be 0 net coulombic attractive force towards the atom on the electron. Then how will the electron be attracted towards the nucleus? Please help me...
 
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From a large distance there is no net coulombic force an thus no attractive force. What do you think will happen as the electron gets much closer?