The reactive cross section is expected to be the largest for the reaction

Concept:

• Harpoon mechanism is a special case of Collison theory proposed for system in which reactants are undergoing electron transfer.
• Rate of halogenation of metals  can be explained quantitatively via this mechanism. 
• Mathematically,

          \(\frac{e^2 }{4\pi \varepsilon _0R_x} =I.E(metal)-EA(halogen)\)

here, R_x is the reactive cross section

I.E is the ionization potential

and E.A. is the electron affinity

Explanation:

• Reactive cross-section is inversely related to \(\Delta E_0\), which is related to ionization potential of metal and  electron affinity of Halogen as:

\(\Delta E_0 = I.P(metal)- E.A(halogen) \)

• Halogen is in all case is same, therefore, relative cross section can be compared by comparing the Ionization potential of metal. The metal with lowest Ionization potential will give largest reaction cross section value for the reaction.
• Down the group, ionization potential of metal decrease. Rb has lowest Ionization value. Thus, halogenation of Rb will have largest reactive cross section value.

Conclusion:

The reactive cross section is expected to be the largest for the reaction:

\(Rb + Cl_2 \rightarrow RbCl +Cl \)