Photoelectric Effects and deBroglie Equation: Practice Problem & Solution
27. A 5 watt source emits monochromatic light of wavelength $5000 \mathring{A}$ . When placed 0.5 m away, it liberates photoelectrons from a photosensitive metallic surface. When the source is moved to a distance of 1.0 m, the number of photoelectrons liberated will be reduced by a factor of (2007)
Solution Explained:
To solve this problem, we apply the core principles of Photoelectric Effects and deBroglie Equation. Understanding the underlying formula is key to arriving at the correct answer below:
The intensity of light $I$ is inversely proportional to the square of the distance $r$ from a point source, so $I \propto \frac{1}{r^2}$ . When the distance is doubled from $0.5 m$ to $1.0 m$ , the intensity becomes $\frac{1}{4}$ of its initial value. Since the number of photoelectrons liberated is directly proportional to intensity, it will also be reduced by a factor of 4.
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