Step 1: Understanding the Concept:
The photoelectric effect describes the emission of electrons from a metal surface when light shines on it. Einstein's photoelectric equation uses the law of conservation of energy to explain this phenomenon. The stopping potential ($V_0$) is the negative voltage required to stop the fastest-moving photoelectrons from reaching the collector plate, reducing the photocurrent to zero.
Step 2: Key Formula or Approach:
Einstein's photoelectric equation is given by:
$$ K_{\max} = h\nu - \phi_0 $$
Where:
- $K_{\max}$ is the maximum kinetic energy of the emitted photoelectrons.
- $h\nu$ is the energy of the incident photon (with frequency $\nu$).
- $\phi_0$ is the work function of the metal.
The maximum kinetic energy relates directly to the stopping potential ($V_0$) by the equation:
$$ K_{\max} = eV_0 \implies eV_0 = h\nu - \phi_0 \implies V_0 = \left(\frac{h}{e}\right)\nu - \frac{\phi_0}{e} $$
Step 3: Detailed Explanation:
Let's analyze both statements and their logical connection:
- Evaluating the Reason (R): Einstein's equation ($K_{\max} = h\nu - \phi_0$) shows that because Planck's constant ($h$) and the work function ($\phi_0$) are constant values for a given metal, raising the frequency ($\nu$) of incoming light linearly increases the maximum kinetic energy ($K_{\max}$) of the escaping electrons. Thus, Reason (R) is completely true.
- Evaluating the Assertion (A): The assertion states that the stopping potential depends on the frequency of the incident radiation. Looking at the combined equation ($eV_0 = K_{\max} = h\nu - \phi_0$), we can see that if the frequency $\nu$ increases, $K_{\max}$ increases, which requires a higher stopping potential $V_0$ to halt the electrons. This confirms that the stopping potential depends directly on the frequency. Thus, Assertion (A) is completely true.
- Evaluating the Logical Link: Why does the stopping potential depend on the frequency of the incoming light? It happens precisely because the stopping potential is the metric used to measure the maximum kinetic energy ($eV_0 = K_{\max}$). Since an increase in frequency causes an increase in maximum kinetic energy, it directly changes the required stopping potential.
Because the physical mechanism described in the Reason directly explains the dependency stated in the Assertion, the Reason is the correct explanation. This matches option (A).
Step 4: Final Answer:
Both Assertion and Reason are true and Reason is the correct explanation of Assertion.