Question

The stopping potential for a fast moving photo-electron is independent of:

• A. the frequency of incident photon.
• B. the intensity of incident photon.
• C. the wavelength of the incident photon.
• D. type of metals

Hint:

For the photoelectric effect, remember this key distinction: - **Frequency/Wavelength** determines the **Energy** of photoelectrons (\(K_{\text{max}}\), \(V_s\)). - **Intensity** determines the **Number** of photoelectrons (photocurrent).

Answer 1

The Correct Option is B

Step 1: Recall the photoelectric effect equation. Einstein's photoelectric equation relates the maximum kinetic energy (\(K_{\text{max}}\)) of a photoelectron to the frequency of the incident photon (\(f\)) and the work function of the metal (\(\phi\)): \[ K_{\text{max}} = hf - \phi \] where \(h\) is Planck's constant.
Step 2: Relate stopping potential to kinetic energy. The stopping potential (\(V_s\)) is the potential required to stop the most energetic photoelectrons. It is related to the maximum kinetic energy by: \[ e V_s = K_{\text{max}} \] where \(e\) is the elementary charge. Combining the two equations gives: \[ V_s = \frac{h}{e}f - \frac{\phi}{e} \]
Step 3: Analyze the dependencies of the stopping potential. From the equation, we can see that \(V_s\) depends on: - The frequency (\(f\)) of the incident photon. - The wavelength (\(\lambda\)), since \(f = c/\lambda\). - The work function (\(\phi\)), which is a property of the specific metal (type of metals). The intensity of the incident light determines the *number* of photons arriving per unit time, which in turn determines the number of photoelectrons emitted (the photoelectric current). However, it does not affect the energy of individual photons, and thus does not affect the maximum kinetic energy or the stopping potential of the photoelectrons.