For the reaction K + Br₂ → KBr + Br, which follows the harpoon mechanism, the reactive cross section is closest to

(Use  = 2.3 × 10⁻²⁸ J m, Ionization energy of K = 422.5 kJ mol⁻¹, electron affinity of Br₂ = 250 kJ mol⁻¹ and N_A = 6 × 10²³ mol⁻¹)

Concept:

Harpoon mechanism:-

One electron from the metal atom jumps to the nonmetal atom when two reactant molecules—one metal and one nonmetal—approach each other at a distance R (the radius of the cross-section where the collision occurs). The process is known as the Harpoon mechanism, and that electron is known as the Harpoon. Following that, non-metals become negatively charged ions, whereas metals become positively charged ions.

     K + Br2 → KBr + Br

When K approaches Br the valence electron(Harpoon) of K moves into Br.

This mechanism involves the following interactions;

• Ionization Energy ( )
• Electron affinity ( )
• Coulombic interaction ( , R= separation between K⁺  and Br^-)

So the reaction will be energetically favorable when 

Example:

  K + Br2 → KBr + Br

According to the theory,

 , (where R= radius of cross-section in which reaction occurs,  r₁ and r₂ = radius of each reactant molecule

  )

Explanation:-

=

=

= 

Area of cross-section

= 

= 

= 2 × 10−18 m2

Conclusion:-

Hence the correct answer is 2 × 10−18 m2.