Step 1: State the photoelectric effect equation. Einstein's photoelectric equation is \(K_{\text{max}} = hf - \phi\), where \(K_{\text{max}}\) is the maximum kinetic energy of a photoelectron, \(f\) is the frequency of the incident photon, \(\phi\) is the work function of the metal, and \(h\) is Planck's constant.
Step 2: Connect stopping potential to kinetic energy. The stopping potential (\(V_s\)) is the voltage needed to stop the fastest photoelectrons. It is related to maximum kinetic energy by \(e V_s = K_{\text{max}}\), where \(e\) is the elementary charge. Combining these equations yields \(V_s = \frac{h}{e}f - \frac{\phi}{e}\).
Step 3: Examine the factors influencing stopping potential. The stopping potential (\(V_s\)) is determined by:- Photon frequency (\(f\)).- Photon wavelength (\(\lambda\)), since \(f = c/\lambda\).- The metal's work function (\(\phi\)), which is a material property.Light intensity affects the *quantity* of emitted photoelectrons (photoelectric current) by determining the number of photons arriving per unit time. However, it does not influence individual photon energy, and therefore does not alter the maximum kinetic energy or the stopping potential of the photoelectrons.