To tackle this question, we need to understand how the distance of a light source affects both the stopping potential and the saturation current in a photoelectric cell. The photoelectric effect describes how light can eject electrons from a material, and the characteristics of this process can be influenced by the intensity of the light, which diminishes with distance.
Understanding the Photoelectric Effect
The photoelectric effect involves the emission of electrons from a material when it is exposed to light. Two key parameters to consider here are:
- Stopping Potential (Cut-off Voltage): This is the minimum voltage needed to stop the emitted electrons from reaching the anode. It is directly related to the energy of the incoming photons.
- Saturation Current: This is the maximum current that can be measured when all emitted electrons are collected. It depends on the intensity of the light hitting the photoelectric cell.
Effect of Distance on Light Intensity
The intensity of light from a point source decreases with the square of the distance from the source, according to the inverse square law. Mathematically, this can be expressed as:
I ∝ 1/d²
Where I is the intensity and d is the distance from the source. This means that if you double the distance, the intensity becomes one-fourth of its original value.
Calculating Changes in Stopping Potential and Saturation Current
Initially, the light source is at 0.2 m, and we have:
- Stopping Potential = 0.6 V
- Saturation Current = 18.0 mA
When the source is moved to 0.6 m, the distance has increased by a factor of 3 (from 0.2 m to 0.6 m). According to the inverse square law:
New Intensity = Original Intensity / 3² = Original Intensity / 9
Impact on Saturation Current
The saturation current is proportional to the intensity of the light. Therefore, if the intensity decreases to one-ninth of its original value, the new saturation current will be:
New Saturation Current = 18.0 mA / 9 = 2.0 mA
Impact on Stopping Potential
The stopping potential is primarily determined by the energy of the photons, which depends on their frequency rather than intensity. Since the frequency of the monochromatic light source remains unchanged, the stopping potential will remain at:
Stopping Potential = 0.6 V
Final Analysis
Based on the calculations and understanding of the photoelectric effect:
- The stopping potential remains at 0.6 V.
- The saturation current decreases to 2.0 mA, which is not one of the options provided.
However, if we consider the options given in the question, the closest correct answer for the saturation current would be 6.0 mA, which is a miscalculation in the options provided. Thus, the stopping potential will be 0.6 V, and the saturation current will be significantly lower than the original value.
