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The trend in electron affinity is to increase negatively across a group.

Does this mean noble gases' electronegativity is more negative than halogens?

Noble gases should have a positive electron affinity as adding an electron would make it unstable and thus will not happen.

But for halogens the attraction for that one electron to fill up the $\mathrm{p}$ subshell is very strong.

But given the theory that electron affinity increases negatively across the period, does this theory make an exception for noble gases?

Next, what about $\ce{Be}$ and $\ce{Mg}$? Their electron affinities are not negative.

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Not exceptions, but see, theories say that going $L→R$ electron affinity increases up to halogens.

For the noble gases, $\Delta_\mathrm{eg}H$ is positive (energy required). While electron affinity is $0$. Which implies no tendency to lose electrons.

For $\ce{Be}$, the small size and nuclear charge are responsible, which is related to $\ce{Mg}$ due to a diagonal relationship.

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    $\begingroup$ Be and Mg are not diagonally related, and in any event diagonal relationships do not work for electron affinities. Mg lacks an exothermic electron affinity because like Be, it has a closed valence shell and an electron would have to be added to a much higher-energy orbital. $\endgroup$ Oct 19, 2020 at 13:02

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