The photoelectric effect is the phenomenon where electrons are emitted from a material when it is illuminated with light of a certain frequency. The kinetic energy of these emitted electrons can be determined by measuring the stopping potential in an experiment.

The stopping potential is the minimum potential required to stop the emitted electrons from reaching the anode. It is equal to the maximum kinetic energy of the photoelectrons. In this case, the stopping potential is 1.5 V.

To understand why the maximum kinetic energy is equal to the stopping potential, we need to consider the energy conservation principle. The energy of a photon is given by E = hf, where E is the energy, h is Planck's constant, and f is the frequency of the light. When a photon strikes a metal surface, it transfers its energy to an electron, causing the electron to be emitted.

The kinetic energy of the emitted electron can be calculated by subtracting the work function (φ) of the material from the energy of the photon. The work function is the minimum energy required to remove an electron from the material. So, the equation for the maximum kinetic energy (KEmax) is:

KEmax = hf – φ

In the case of the stopping potential, the kinetic energy of the photoelectrons is equal to the energy gained by the electrons due to the potential difference between the cathode and the anode. This can be expressed as:

KEmax = eVs

Where e is the charge of an electron and Vs is the stopping potential.

Since the maximum kinetic energy is equal to the stopping potential, we can equate the two equations:

hf – φ = eVs

Rearranging the equation, we get:

hf = eVs + φ

From this equation, we can see that the maximum kinetic energy (hf) is equal to the stopping potential (eVs) plus the work function (φ). In this case, the stopping potential is given as 1.5 V. Therefore, the maximum kinetic energy is also 1.5 eV. Thus, the correct answer is option A, 1.5 eV.