As the elements of group 17 are considered in order of increasing atomic number, there is an increase in
(1) atomic radius
(2) electronegativity
(3) first ionization energy
(4) number of electrons in the first shell

Alright so the way I see it by definition of increasing atomic number of the halogen family, that means you're going down the periodic table. Therefore, there's an increase in the number of outer shells. The atomic radius would increase because that's basically the distance between the nucleus of the element to the outermost electron. More electron shells=Greater distance=Larger atomic radius

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