Step 1: Recall the concept of Brownian movement.
Brownian movement is the continuous random zig-zag motion of colloidal particles caused by unequal collisions with the molecules of the dispersion medium.
This motion helps maintain the stability of colloidal solutions by preventing the particles from settling under gravity.
Step 2: Effect of particle size.
The intensity of Brownian movement increases as the size of the colloidal particles decreases.
Smaller particles experience less resistance and are more easily displaced by collisions with solvent molecules.
Therefore,
\[
\text{Smaller particle size}
\Rightarrow
\text{Greater Brownian movement}
\]
Step 3: Effect of viscosity of the medium.
Viscosity provides resistance to the motion of colloidal particles.
As viscosity increases, the movement of particles becomes slower.
Hence,
\[
\text{Higher viscosity}
\Rightarrow
\text{Lower Brownian movement}
\]
and
\[
\text{Lower viscosity}
\Rightarrow
\text{Higher Brownian movement}
\]
Step 4: Combine both effects.
For maximum Brownian motion, we require:
Small particle size
and
Low viscosity of the medium
Thus, the most favorable condition is
Smaller size and lesser viscosity
Step 5: Final conclusion.
Hence, the condition that favours the fastest Brownian movement is
\[
\boxed{\text{Smaller size and lesser viscosity}}
\]
Therefore, option (2) is correct.