Question

Pick out the INCORRECT statement from the following:

• A. the value of stopping potential is the same for radiations of all frequencies
• B. the stopping potential is more negative for the incident radiation of higher frequency
• C. the value of saturation current depends on the intensity of incident radiation
• D. the value of saturation current is independent of frequency of incident radiation
• E. the emission of electrons is instantaneous

Hint:

Stopping potential depends only on frequency, not intensity.

Answer 1

The Correct Option is A

Step 1: Understanding the Photoelectric Effect:
The photoelectric effect is the emission of electrons from a material when it is exposed to electromagnetic radiation of a sufficiently high frequency. Its key features are explained by treating light as a stream of particles called photons.
Step 2: Key Formula - Einstein's Photoelectric Equation:
The maximum kinetic energy (\(K_{max}\)) of the emitted photoelectrons is given by:
\[ K_{max} = hf - \phi \] where \(h\) is Planck's constant, \(f\) is the frequency of the incident radiation, and \(\phi\) is the work function of the material.
The stopping potential (\(V_s\)) is the retarding potential required to stop the most energetic electrons. It is related to \(K_{max}\) by:
\[ K_{max} = eV_s \] Combining these gives the relationship between stopping potential and frequency:
\[ eV_s = hf - \phi \quad \Rightarrow \quad V_s = \left(\frac{h}{e}\right)f - \frac{\phi}{e} \] Step 3: Evaluating Each Statement:
(A) The equation \(V_s = (h/e)f - (\phi/e)\) clearly shows that the stopping potential \(V_s\) is a linear function of the frequency \(f\). It is not the same for all frequencies. Therefore, this statement is INCORRECT.
(B) As the frequency \(f\) increases, the stopping potential \(V_s\) also increases linearly. A higher stopping potential means a more negative voltage is required. This statement is correct.
(C) The intensity of light corresponds to the number of photons arriving per second. More photons eject more electrons, leading to a higher photoelectric current. The maximum current is the saturation current. Thus, saturation current depends on intensity. This statement is correct.
(D) The saturation current depends on the number of emitted electrons, not their individual energy. The energy of electrons depends on frequency, not the number. Thus, saturation current is independent of frequency (as long as \(f\) is above the threshold). This statement is correct.
(E) The photoelectric emission is a one-photon, one-electron process with no significant time delay. It is considered an instantaneous process. This statement is correct.
Step 4: Final Answer:
The question asks for the INCORRECT statement, which is (A).