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The Photoelectric Effect: A Foundational Concept in Quantum Science
What Is the Photoelectric Effect?
The photoelectric effect occurs when light shining on a metal surface ejects electrons. This phenomenon proves the particle-like nature of light.
Key Principles of the Photoelectric Effect
Einstein’s Equation
\[ E = hf = \phi + KE_{\text{max}} \]
Where:
- \( E \): Energy of the photon (J)
- \( h = 6.63 \times 10^{-34} \, \text{J·s} \): Planck’s constant
- \( f \): Frequency of the light (Hz)
- \( \phi \): Work function (J)
- \( KE_{\text{max}} \): Maximum kinetic energy of ejected electrons (J)
Threshold Frequency (\( f_0 \))
For electrons to be ejected, the light’s frequency must exceed the threshold frequency:
\[ f_0 = \frac{\phi}{h} \]
Example Problem
Light with a wavelength of \( 400 \, \text{nm} \) shines on a metal with a work function of \( 2 \, \text{eV} \). Determine if electrons are ejected and calculate their maximum kinetic energy.
- Photon Energy (\( E \)):
\[ E = \frac{hc}{\lambda} = \frac{(6.63 \times 10^{-34})(3.0 \times 10^8)}{400 \times 10^{-9}} \approx 3.1 \, \text{eV} \] - Since \( E > 2 \, \text{eV} \), electrons are ejected.
- Kinetic Energy:
\[ KE_{\text{max}} = E – \phi = 3.1 – 2 = 1.1 \, \text{eV} \]
Applications of the Photoelectric Effect
Solar Panels
Convert sunlight into electrical energy using the photoelectric effect.
Photodetectors
Measure light intensity in cameras and sensors.
Quantum Theory
The photoelectric effect supports the wave-particle duality of light.
Common Mistakes in Photoelectric Effect Problems
- Forgetting to convert units (e.g., nm to m or eV to J)
- Confusing photon energy with work function
- Mixing up frequency and wavelength in calculations
Practice Questions
- A metal surface has a work function of \( 3 \, \text{eV} \). Light with a frequency of \( 8 \times 10^{14} \, \text{Hz} \) shines on it. Calculate the maximum kinetic energy of ejected electrons.
- Explain the importance of the photoelectric effect in quantum theory.
- Describe one application of the photoelectric effect in modern technology.