When electrons have been removed from an atom or molecule, it's been ionised. The energy you need to remove the first electron is called the first ionisation energy (or often just ionisation energy).
The first ionisation energy is the energy needed to remove 1 electron from each atom in 1 mole of gaseous atoms to form 1 mole of gaseous 1+ ions.
You can write equations for this process - here's the equation for the first ionisation of oxygen:
O (g) --> O+ (g) + e-
Here are a few rather important points about ionisation energies:
1) You must use the gas state symbol (g), because the ionisation energies are measured for gaseous atoms.
2) Always refer to 1 mole of atoms, as stated in the definition, rather than to a single atom.
3) The lower the ionisation energy, the easier it is to form an ion.
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