Step 1: Understanding the Concept:
This question relates to the laws of the photoelectric effect. The intensity of light is related to the number of photons incident on a surface per unit area per unit time. The photoelectric current is due to the flow of emitted photoelectrons.
Step 2: Detailed Explanation:
In the quantum picture of light, the intensity of radiation is proportional to the number of photons incident per second. The photoelectric effect is a one-to-one interaction: one incident photon ejects one electron (provided the photon has enough energy, i.e., its frequency is above the threshold frequency).
Therefore:
- A higher intensity means more photons are hitting the surface per second.
- More incident photons will lead to more photoelectrons being ejected per second.
- More photoelectrons ejected per second means a larger flow of charge, which constitutes a larger photoelectric current.
This establishes a direct proportionality:
Intensity of incident radiation Number of photons per second Number of photoelectrons emitted per second Photoelectric current. Let's evaluate the options based on this understanding:
1. Incorrect. The number of photoelectrons depends on the number of photons (intensity), not the energy of each photon (frequency).
2. Incorrect. It's a direct proportionality, not inverse.
3. Correct. As explained above, the number of photoelectrons emitted per second is directly proportional to the intensity of the incident radiation.
4. Incorrect. There is a direct and fundamental relationship.
Step 3: Final Answer:
The photoelectric current being proportional to the number of photoelectrons emitted per second implies that this number is directly proportional to the intensity of the incident radiation.