Answer the question on basis of passage given below:

Lyophobic sols like those of metals (Au, Ag, etc) are unstable and are easily precipitated by addition of electrolytes. However, it is observed that the addition of certain lyophilic colloids like gums, soaps, gelatine, etc. to lyophobic colloids (like a metal sol) render lyophobic colloids difficult to coagulate by the addition of electrolytes. The process is known as 'protection' and the lyophilic colloids are termed as Protective colloids. It is believed that the protective action of the lyophilic colloids is due to the covering up of the particles of the lyophobic colloid by those of the lyophilic colloid. Evidently, smaller the gold number of a protective colloid, the greater is its protective action.

Critical micelle concentration of soap solutions lie in the range of:

\(10^{-4}\) to \(10^{-3}\) \(M\)

The correct answer is option 3. \(10^{-4}\) to \(10^{-3}\) \(M\).

The critical micelle concentration (CMC) of soap solutions typically lies in the range of \(10^{-4}\) to \(10^{-3}\) \(M\).

The critical micelle concentration (CMC) is the concentration at which micelles start to form in a solution of surfactants (such as soap). Below the CMC, individual surfactant molecules are present in the solution. However, as the concentration of surfactant increases and reaches the CMC, micelles begin to form spontaneously. These micelles consist of aggregates of surfactant molecules, with their hydrophobic tails clustered together in the core and their hydrophilic heads facing outward, surrounded by the solvent.

In the case of soap solutions, the CMC typically falls in the range of \(10^{-4}\) to \(10^{-3}\) \(M\) (molarity). This range indicates the concentration threshold at which micelle formation becomes significant and starts to dominate the behavior of the solution.