Step 1: Understanding the Concept:
The photoelectric effect is the emission of electrons from a metal surface when it is struck by light of a certain minimum frequency.
According to Einstein's photon theory, light is made of discrete energy packets called photons. Each photon carries energy proportional to its frequency.
When a photon hits an electron in the metal, it transfers its entire energy to that electron.
Part of this energy is used to overcome the binding force of the metal (the work function, \(\phi\)), and the remaining energy becomes the kinetic energy of the emitted electron.
The "stopping potential" (\(V_{0}\)) is the minimum negative voltage applied to the collector plate that is just strong enough to stop even the fastest-moving electrons from reaching it, thus bringing the current to zero.
Therefore, the stopping potential is a direct measure of the maximum kinetic energy (\(K_{max}\)) of the photoelectrons.
Step 2: Key Formula or Approach:
Einstein’s photoelectric equation is:
\[ h\nu = \phi + K_{max} \]
Substituting \(K_{max} = eV_{0}\) (where \(e\) is the charge of an electron):
\[ h\nu = \phi + eV_{0} \]
Rearranging for \(V_{0}\):
\[ V_{0} = \left( \frac{h}{e} \right) \nu - \frac{\phi}{e} \]
Where:
\(\nu\) = frequency of incident light
\(h\) = Planck's constant
\(\phi\) = work function of the metal
Step 3: Detailed Explanation:
From the derived equation \(V_{0} = \frac{h}{e}\nu - \frac{\phi}{e}\), we can analyze the factors:
1. Frequency: Stopping potential is directly and linearly dependent on the frequency of the incident light. As frequency increases, the photon energy increases, resulting in higher kinetic energy for the electrons. Thus, a higher stopping potential is required to stop them.
2. Intensity: Intensity refers to the number of photons hitting the surface per second. Increasing intensity increases the number of emitted electrons (photocurrent), but it does not change the energy of individual photons. Consequently, intensity has no effect on the maximum kinetic energy or the stopping potential.
3. Distance/Area: Changing the distance or the area of the metal only affects the intensity of light reaching the surface. As discussed, these do not change the energy of individual electrons.
This discovery was crucial because it disproved the classical wave theory of light, which predicted that higher intensity should lead to higher electron energy.
The fact that stopping potential depends only on frequency and the material's property (work function) is a cornerstone of quantum mechanics.
Step 4: Final Answer:
The stopping potential depends solely on the frequency of the incident light and the nature of the material.
Therefore, the correct option is (B).