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The increasing order of reactivity among group 1 elements is \[Li < Na < Rb < Cs\], whereas that among group 17 elements is $F > Cl > Br > I$. Explain?

Answer
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Hint: Group one elements are called alkali metals and according to the electronic configuration there is only one electron in the outermost shell. Group 17 elements are called halogens and according to the electronic configuration there are seven electrons in the outermost shell.

Step by step answer: As it is given that reactivity among group 1 elements is \[Li < Na < Rb < Cs\]and reactivity of these elements means the power of removing outermost 1 electron as there is only 1 electron is present, which is inversely proportional to the ionization enthalpy.

Ionization enthalpy is that minimum amount of energy required to lose electrons from the outermost shell.

This energy is inversely proportional to the size of the atom, because as the size of the atom increases attraction between the nucleus and outermost electron decreases.
From the above discussion it is clear that reactivity of group 1 elements is directly proportional to the atomic size.

$Reactivity \alpha AtomicSize \alpha \dfrac{1}{{IonizationEnthalpy}}$

In the question it is also given that reactivity among group 17 elements is $F > Cl > Br > I$ and reactivity of these elements means the power of accepting 1 electron from outside for the completion of octet, which is directly proportional to the electronegativity of the atom.
Electronegativity of any element is the power of attracting electrons towards itself.
Electronegativity is inversely proportional to the atomic size of the atom, because as the size of atom is small then there is appreciable nuclear attraction force towards the upcoming electron. From the above discussion it is clear that reactivity of group 17 elements is inversely proportional to the atomic size.

 $Reactivity \alpha Electronegativity \alpha \dfrac{1}{{AtomicSize}}$

Note: In this type of questions you may get confused as to where you have to deal with ionization enthalpy and electronegativity. So to get rid of this confusion you have to know about the electronic configuration of a given element and whenever there is a condition of losing an electron then you will do question according to ionization enthalpy and whenever there is accepting of electron then you will do question according to electronegativity.