When photons of energy 6 eV fall on the surface, the maximum kinetic energy of the photoelectrons emitted is 4 eV. We need to find the stopping potential.


- The photoelectric effect refers to the emission of electrons from a metal surface when light falls on it.
- According to the photoelectric effect, electrons can be emitted from a metal surface only if the incident photons have sufficient energy.
- The kinetic energy of the emitted photoelectrons depends on the energy of the incident photons.


- The energy of a photon is given by the equation E = hf, where E is the energy, h is Planck's constant (6.63 x 10^-34 J.s), and f is the frequency of the light.
- The kinetic energy of a photoelectron is given by the equation KE = E - W, where KE is the kinetic energy, E is the energy of the incident photon, and W is the work function of the metal (the minimum energy required to remove an electron from the metal surface).


- The stopping potential is the minimum potential difference required to stop the photoelectrons from reaching the collector plate in a photoelectric experiment.
- The stopping potential can be found by equating the kinetic energy of the photoelectrons to the potential energy gained due to the electric field.
- The potential energy gained due to the electric field is given by the equation PE = qV, where PE is the potential energy, q is the charge of the electron (1.6 x 10^-19 C), and V is the stopping potential.


- In this case, the energy of the incident photons is 6 eV, and the maximum kinetic energy of the photoelectrons is 4 eV.
- The work function can be found by subtracting the maximum kinetic energy from the energy of the incident photons: W = E - KE = 6 eV - 4 eV = 2 eV.
- Now, we can find the stopping potential by equating the potential energy gained due to the electric field to the kinetic energy of the photoelectrons: qV = KE = 4 eV.
- Solving for V, we get V = KE/q = 4 eV / (1.6 x 10^-19 C) ≈ 2.5 x 10^19 V.
- Converting the potential to volts, we have V ≈ 2.5 x 10^19 eV / 6.24 x 10^18 V/eV ≈ 4 V.


Therefore, the stopping potential is approximately 4 V, which corresponds to option C.