The graph between intensity of light falling on a metallic plate (l) with the current (i) generated is

Options

A.
B.
C.
D.

Answer

To solve the problem of determining the graph between the intensity of light falling on a metallic plate (I) and the current (i) generated, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Intensity and Power**:
- Intensity (I) is defined as power (P) per unit area (A). Mathematically, it can be expressed as:
\[ I = \frac{P}{A} \]
- Power (P) can be defined as energy (E) per unit time (t):
\[ P = \frac{E}{t} \]

2. **Relating Intensity to Number of Photons**:
- If we consider the energy of a single photon, we can say that the total energy for n photons is:
\[ E = n \cdot e \]
- Therefore, substituting this into the power equation gives:
\[ I = \frac{n \cdot e}{A \cdot t} \]
- This shows that intensity is directly proportional to the number of photons (n).

3. **Understanding Current**:
- Current (i) is defined as charge (Q) per unit time (t):
\[ i = \frac{Q}{t} \]
- The charge (Q) can be related to the number of electrons ejected by the photons. Since each photon can eject one electron, we can say:
\[ Q = n \cdot e \]
- Substituting this into the current equation gives:
\[ i = \frac{n \cdot e}{t} \]

4. **Establishing the Relationship**:
- From the previous steps, we can see that both intensity (I) and current (i) are directly proportional to the number of photons (n):
\[ I \propto n \quad \text{and} \quad i \propto n \]
- Therefore, we can conclude that:
\[ I \propto i \]
- This indicates a linear relationship between intensity and current.

5. **Graph Characteristics**:
- Since both intensity and current are directly proportional, the graph will be a straight line.
- Additionally, if there is no intensity (I = 0), there will be no current (i = 0). Thus, the graph must pass through the origin.

6. **Choosing the Correct Graph**:
- Among the options provided, we need to select the graph that is linear and starts from the origin. This leads us to conclude that the correct graph is option number two.

### Final Answer:
The graph between the intensity of light falling on a metallic plate and the current generated is a straight line passing through the origin (option number two).