Step 1: Understanding the Concept:
The photoelectric effect demonstrates that light consists of particles (photons). The frequency of light determines the energy per electron, while intensity determines the total number of electrons emitted.
Step 2: Detailed Explanation:
(A) Incorrect: Wave theory failed because it predicted emission would depend on intensity rather than frequency.
(B) Incorrect: Maximum kinetic energy depends strictly on the frequency of light ($K_{max} = h\nu - \phi$).
(C) Incorrect: Stopping potential ($V_0$) depends on kinetic energy, which depends on both frequency and work function ($eV_0 = h\nu - \phi$).
(D) Correct: Higher intensity means more photons per second, leading to more photoelectrons per second, which increases the total saturation current.
Step 3: Final Answer:
Statement (D) is the correct statement.