Group 1 metals melting/boiling points decrease down the group because the metallic bonding between the ions and the electrons produces a weak attraction and its reactivity increases as the outer electron is easily lost. Whereas with group 7 halogens the reactivity decreases down the group due to the fact that its trying to gain an electron so that it has a full outer shell but as the atom becomes bigger the attractive force needed to gain an electron decreases so it becomes harder to gain a new electron and they also have high melting/boiling points as they go down but I cant seem to figure out why the melting/boiling point is inversely proportional to the reactivity of the metal
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For the halogens, the strength of the intermolecular forces (van der waals forces) increases as the diatomic molecule becomes bigger, as there are more electrons, creating a greater instantaneous dipole.
(This is not a super scientific explanation, if anyone can correct me or add any details please do!)
The metallic bonding gets weaker because the alkali metals only have 1 delocalised electron and the melting/boiling points decrease because the intermolecular forces become weaker and therefore it requires more energy to overcome the forces