Physics Dual Nature of Radiation and Matter 1 Mark
Appeared in: 2024 (3 sets)
Assertion (A) : Photoelectric current increases with an increase in intensity of incident radiation, for a given frequency of incident radiation and the accelerating potential. Reason (R) : Increase in the intensity of incident radiation results in an increase in the number of photoelectrons emitted per second and hence an increase in the photocurrent.
✓ Verified CBSE Marking Scheme Official Evaluation Steps & EL10 Insight

Correct Option: Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Step 1 (Foundational Principle): [0.25 Mark]
The photoelectric effect is governed by the particle nature of light (photons). The intensity of incident radiation ($I$) is directly proportional to the number of photons incident per unit area per unit time ($N$). According to Einstein's photoelectric equation:

$$K_{max} = h\nu - \Phi_0$$

Where $h\nu$ is the energy of a single photon and $\Phi_0$ is the work function.

Step 2 (Logical Deduction): [0.50 Mark]
Since the frequency ($\nu$) is kept constant, the energy of each individual photon ($E = h\nu$) remains constant. When intensity ($I$) increases, the number of photons striking the metal surface per second increases. Given that one photon ejects one photoelectron (provided $\nu > \nu_0$), the rate of emission of photoelectrons ($n$) increases:

$$n \propto I$$

The photoelectric current ($i$) is defined as the rate of flow of charge ($q$):

$$i = \frac{q}{t} = \frac{n \cdot e}{t}$$

As $n$ increases, the total charge flowing per unit time increases, leading to a higher photocurrent.

Step 3 (Final Conclusion): [0.25 Mark]
Since the increase in intensity directly increases the number of photoelectrons emitted per second, the photocurrent increases. Thus, Assertion (A) is true, and Reason (R) provides the correct physical explanation for this observation.

💡 EL10 Concept Insight: Think of light as a stream of tennis balls hitting a wall; if you throw more balls at the same speed (increasing intensity), more balls bounce off the wall every second, which is exactly like having more electrons flowing to create a stronger current.