Question Details

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

Options

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.

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Correct Answer :

Option C

the number of photoelectrons emitted per second is directly proportional to the intensity of incident radiation.

Solution :

The correct option is: the number of photoelectrons emitted per second is directly proportional to the intensity of incident radiation.

Let us understand this step-by-step through the principles of the photoelectric effect:
1. Electric Current and Charge Carrier Flow: Electric current is defined as the rate of flow of electric charge. In the photoelectric effect, the current (known as photoelectric current) is constituted by the flow of emitted photoelectrons. Thus, the photoelectric current is directly proportional to the number of photoelectrons emitted per second.
2. Concept of Intensity: The intensity of the incident radiation refers to the energy falling on a unit area per unit time. For a light source of a given frequency, the intensity is directly proportional to the number of photons incident on the surface per second. Each photon carrying energy E=hν interacts with a single electron.
3. Photon-Electron Interaction: According to Einstein's photoelectric theory, the emission of photoelectrons is a one-to-one interaction. One incident photon interacts with only one electron in the metal. If the energy of the incident photon is greater than the work function of the metal, a photoelectron is emitted.
4. Connecting the Dots:
- Increasing the intensity of incident radiation increases the number of photons hitting the metal surface per second.
- Since one photon can liberate at most one photoelectron, a higher number of incident photons per second leads to a larger number of photoelectrons being emitted per second.
- Consequently, the photoelectric current increases.
Therefore, the statement implies that the number of photoelectrons emitted per second is directly proportional to the intensity of the incident radiation.

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