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How can electron affinity be negative?

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Hint: We know that electron affinity is the change in enthalpy which takes place when a gaseous atom gains an extra electron to form a monovalent anion also in the gaseous state. It is also known as electron gain enthalpy.

Complete step by step answer:
Let’s discuss the negative and positive electron affinity.
Positive electron affinity means energy is consumed when an extra electron is added to the neutral atom. In many cases such as noble gases and alkaline earth metals, there is the presence of completely filled valence shells of an atom. These atoms do not have any urge to gain extra electrons and energy has to be supplied in such cases. That means the electron gain enthalpy will be positive. For example, when an electron is added to the neon atom, electron affinity is positive.
${\text{Ne}}\left( g \right) + {e^ - } \to {\text{N}}{{\text{e}}^ - }\left( g \right)$
${\Delta _{eg}}H = 116\,{\text{kJ}}\,\,{\text{mo}}{{\text{l}}^{ - 1}}$
Negative electron affinity means energy is released when an extra electron is added to the neutral atom. For example, when an extra electron is added to an oxygen atom, some amount of energy is released. So, oxygen has negative electron affinity.
${\text{O}}\left( g \right) + {e^ - } \to {{\text{O}}^ - }\left( g \right)$
${\Delta _{eg}}H = - 141\,\,{\text{kJ}}\,\;{\text{mo}}{{\text{l}}^{ - 1}}$
Chlorine is the element which has the highest negative electron affinity that means more energy is released in addition of an electron to the chlorine atom in comparison to other atoms.

Note: It is to be noted that the phenomenon ionization energy is opposite to the electron affinity. Ionization energy is the minimum amount of energy required to remove the most loosely bound electron from a natural isolated gaseous atom in its ground state to form a cation also in the gaseous state.