Question

If the ionic radii of K+ and F- are nearly the same (i.e, 1.34 angstrom), then the atomic radii of K and F respectively are :

1) 1.34 °A , 1.34 °A
2) 0.72 °A , 1.96 °A
3) 1.96 °A , 0.72 °A
4) 1.96 °A , 1.34 °A

Answer 1

if any atom loss electron then their radius will be decrease so , it means radius of atom k has more value then k+ ion
and if any atom gain electron then their size increases it means radius of F atom is smaller then F- ion

now due to above conclusion , option(3) is correct answer .

Answer 2

When Potassium atom loses an electron, the radius reduces. As the outermost electron orbit (largest) is gone.  Clearly, when K+ ion gains an electron its size increases.
Approx sizes :   K:  210-240 pm ...  K+ ion:  140-150 pm

When Fluorine atom gains an electron, the size increases due to its orbit and due to more electrons in the outermost orbit. (repulsion)...
So Fluorine ion loses an electron , size decreases.
          F:  50 - 60 pm...   F- :  110 -120 pm