Question

The photoelectric current is directly proportional to the number of photo electrons emitted per second. This implies that

• A. the number of photoelectrons emitted per second is equal to the frequency of incident radiation.
• B. the number of photoelectrons emitted per second is inversely proportional to the intensity of incident radiation.
• C. the number of photoelectrons emitted per second is directly proportional to the intensity of incident radiation.
• D. the number of photoelectrons emitted per second is not related to the intensity of incident radiation.

Hint:

Remember the two key aspects of the photoelectric effect: 1. Intensity determines the number of photoelectrons (and thus the current). 2. Frequency determines the maximum kinetic energy of the photoelectrons. This separation of roles is a cornerstone of the quantum explanation of the effect.

Answer 1

The Correct Option is C

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 \(\propto\) Number of photons per second \(\propto\) Number of photoelectrons emitted per second \(\propto\) 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.