The electron and the nucleus are pulled in opposite directions.
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In a classical picture, when the atom is placed in an external electric field, the electron and the nucleus are pulled in opposite directions because they have opposite signs. This may rip the electron from the nucleus if the electron is not strongly bound, or if the external field is strong enough. The strength of the electric field required to remove an electron depends on how tightly bound a particular electron is. For example, outer so-called valence electrons are farther away from the nucleus and shielded electrically from the nucleus by core electrons. A relatively weak electric field can cause such an electron to be ripped away from the atom.