Which of the following pairs have linear relationships between themselves when photoelectrons are emitted from a surface ?

Options

A. Intensity of incident radiation and stopping potential
B. Photoelectric current and frequency of incident radiation
C. Photoelectric current and the potential difference between the emitter (cathode ) and collector (anode)
D. Frequency of incident radiation and the stopping potential

Answer

To determine which pairs have linear relationships when photoelectrons are emitted from a surface, we need to analyze the relationships between the different variables involved in the photoelectric effect.

### Step-by-Step Solution:

1. **Understanding the Photoelectric Effect**:
The photoelectric effect describes how electrons are emitted from a material when it is exposed to light (photons). The key variables involved are the intensity of incident radiation, frequency of the incident radiation, stopping potential, and photoelectric current.

2. **Analyzing Each Pair**:
- **Pair 1: Intensity of stopping potential**: This is not a standard relationship; stopping potential is typically related to the energy of the emitted electrons, not directly to intensity.
- **Pair 2: Photoelectric current and frequency**: The photoelectric current increases with intensity but is not directly proportional to frequency. The frequency must exceed a threshold value for electrons to be emitted.
- **Pair 3: Photoelectric current and potential difference**: The photoelectric current increases linearly with potential difference until saturation current is reached.
- **Pair 4: Frequency of incident radiation and stopping potential**: Stopping potential is related to the frequency of the incident radiation through the equation \( eV_s = hf - \phi \). This relationship is linear.
- **Pair 5: Intensity of incident radiation and stopping potential**: Stopping potential does not depend on intensity; it depends on frequency.
- **Pair 6: Photoelectric current and intensity**: The photoelectric current is directly proportional to the intensity of the incident radiation, assuming the frequency is above the threshold.
- **Pair 7: Photoelectric current and frequency**: As mentioned earlier, this is not a linear relationship.

3. **Identifying Linear Relationships**:
From the analysis:
- **Linear relationships**:
- Photoelectric current and potential difference (Pair 3)
- Frequency of incident radiation and stopping potential (Pair 4)
- Photoelectric current and intensity (Pair 6)

### Conclusion:
The pairs that have linear relationships when photoelectrons are emitted from a surface are:
- Photoelectric current and potential difference
- Frequency of incident radiation and stopping potential
- Photoelectric current and intensity