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A photo-cell is illuminated by a source of light,which is placed at a distance d from the cell.If the distance become d/2, then number of electrons emited per second will be
A photo-cell is illuminated by a source of light,which is placed at a distance d from the cell.If the distance become d/2, then number of electrons emited per second will be
Updated On: Jul 18, 2024
- Remain same
- Four times
- Two times
- One-fourth
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The Correct Option is B
Solution and Explanation
The correct option is(B): Four times
The intensity (I) of light is given by the formula: I = E / (At)
Here, E represents the total energy of the light source, A is the area of the illuminated surface, and t is the time.Thus, we can express I as:
I = (4πr^2 tE) / (4πr^2)
Now, consider the ratio of two intensities, I2/I1:
(I2/I1) = [(4πr2 tE) / (4πr1^2 tE)]
Simplifying this expression:
(I2/I1) = (r1^2 / r2^2)
This ratio shows that I2/I1 is equal to 1/4. This relationship indicates that the number of photoelectrons emitted is directly proportional to the intensity of light. Therefore, the number of electrons emitted one-quarter of the initial number.
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Concepts Used:
Photoelectric Effect
When light shines on a metal, electrons can be ejected from the surface of the metal in a phenomenon known as the photoelectric effect. This process is also often referred to as photoemission, and the electrons that are ejected from the metal are called photoelectrons.
Photoelectric Effect Formula:
According to Einstein’s explanation of the photoelectric effect :
The energy of photon = energy needed to remove an electron + kinetic energy of the emitted electron
i.e. hν = W + E
Where,
- h is Planck’s constant.
- ν is the frequency of the incident photon.
- W is a work function.
- E is the maximum kinetic energy of ejected electrons: 1/2 mv².
Laws of Photoelectric Effect:
- The photoelectric current is in direct proportion to the intensity of light, for a light of any given frequency; (γ > γ Th).
- There exists a certain minimum (energy) frequency for a given material, called threshold frequency, below which the discharge of photoelectrons stops completely, irrespective of how high the intensity of incident light is.
- The maximum kinetic energy of the photoelectrons increases with the increase in the frequency (provided frequency γ > γ Th exceeds the threshold limit) of the incident light. The maximum kinetic energy is free from the intensity of light.
- The process of photo-emission is an instantaneous process.
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