Dual Nature Of Radiation

In the photoelectric effect, the saturation current is determined by the number of photoelectrons emitted per unit time, which is directly proportional to the intensity (energy per unit area per unit time) of the incident light.When the frequency of the incident light is changed from red to blue, while keeping the energy per unit area per unit time (intensity) of the incident radiation fixed, the following happens:1. Energy of Photons: Blue light has a higher frequency than red light, so the energy of each photon of blue light ( , where is the frequency) is greater than that of red light photons.2. Number of Photons: Since the intensity (total energy per unit area per unit time) is kept constant, if the energy of each photon increases (as in the case of blue light), the number of photons hitting the surface per unit time must decrease to keep the total energy per unit area per unit time constant.3. Photoelectrons Emission: The number of photoelectrons emitted per unit time (and hence the saturation current) depends on the number of incident photons. With a higher energy per photon (blue light), fewer photons are needed to maintain the same intensity, resulting in fewer photoelectrons emitted.Thus, the correct answer is: D. Saturation current for blue color light is smaller than red color light

The number of electrons ejected by the photoelectric effect is influenced by the number of incident photons on the material's surface. This number of photons is directly related to the light's intensity.The intensity of the light ( ) directly correlates with the number of photons reaching the surface per unit of time. As a result, a higher light intensity indicates more photons are available to interact with the surface in the same amount of time.Assuming the intensity remains constant over time, the emission rate of electrons remains stable, resulting in a constant photocurrent. Given that , the photocurrent will be greatest for , followed by , and lowest for . This is because the intensity determines the number of photons, and thus the number of possible electron emissions, which directly affects the photocurrent.

Given:Stopping Potential for : Stopping Potential for : Photoelectric Equation: For Wavelength : Rearranging gives: For Wavelength : This simplifies to: Now, equating Equation 1 and Equation 2: Solving gives: Therefore: Thus, the work function of the material is .