Correct Answer  Option 3 :
\(L_e ~=~\frac{L}{2}\)
Explanation:
According to Euler buckling load is determined by:
\({P_b} = \frac{{{\pi ^2}E{I_{}}}}{{L_e^2}}\)
where P_{b} = Buckling load, E = Young’s modulus of elasticity, Imin = Minimum moment of inertia, Le = Effective/Equivalent length
Buckling load for various end conditions is given in the table below.
End conditions

Le

Buckling load 
Both ends hinged

Le = L

\({P_b} = \frac{{{\pi ^2}E{I_{}}}}{{L^2}}\) 
Both ends fixed

\({L_e} = \frac{L}{2}\)

\({P_b} = \frac{{{4\pi ^2}E{I_{}}}}{{L^2}}\) 
One end fixed and another end is free

Le = 2L

\({P_b} = \frac{{{\pi ^2}E{I_{}}}}{{4L^2}}\) 
One end fixed and another end is hinged

\({L_e} = \frac{L}{{\sqrt 2 }}\)

\({P_b} = \frac{{{\pi ^2}E{I_{}}}}{{2L^2}}\) 