Correct Option: (C) [Graph showing I increasing linearly with Intensity]
Step 1 (Governing Law & Definition): [1/3 Mark]
According to Einstein’s photoelectric equation and the particle nature of light, the photoelectric current ($I$) is directly proportional to the number of photoelectrons emitted per unit time. Since each incident photon ejects one photoelectron (provided the frequency $\nu > \nu_0$), the number of photoelectrons emitted is directly proportional to the number of incident photons per unit time, which defines the intensity ($P$) of the incident light.
$$I \propto N_{photons} \implies I \propto \text{Intensity}$$Step 2 (Step-by-Step Mathematical Working): [1/3 Mark]
Let $n$ be the number of photons incident per unit area per unit time, and $A$ be the area of the metal surface. The intensity $I_{nt}$ is given by:
$$I_{nt} = \frac{n \cdot h\nu}{A}$$Since the photoelectric current $I$ is given by $I = e \cdot \frac{dN}{dt}$ (where $\frac{dN}{dt}$ is the rate of emission of photoelectrons), and $\frac{dN}{dt} \propto n$, we substitute the proportionality:
$$I = k \cdot I_{nt}$$Where $k$ is a constant representing the quantum efficiency of the metal surface. This represents a linear equation of the form $y = mx$, where the slope $m = k$.
Step 3 (Final Concluded Answer): [1/3 Mark]
As the intensity of incident light increases, the number of photons striking the metal surface increases linearly. Consequently, the number of emitted photoelectrons increases linearly, resulting in a linear increase in the photoelectric current $I$. Therefore, the graph is a straight line passing through the origin.
💡 EL10 Concept Insight:
Think of light as a stream of tiny energy balls (photons). If you throw more balls at a wall (increasing intensity), more balls will bounce off; similarly, if you shine more light on a metal, more electrons get knocked off, creating a stronger electric current!