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Understanding Einstein’s Photoelectric Equation and Millikan’s Validation
The discovery and explanation of the photoelectric effect marked a turning point in our understanding of quantum mechanics. Albert Einstein’s groundbreaking explanation in 1905, which earned him the Nobel Prize in Physics in 1921, introduced the world to the quantum nature of light. Later, Robert A. Millikan meticulously tested Einstein’s photoelectric equation, offering experimental confirmation of its validity. Let’s delve into these milestones and their significance and understand the Einstein’s Photoelectric Equation And Millikan’s Validation for the equation.
This question appeared in the “Physics Class 12 CBSE Question Paper 2024 – Section C“
Einstein’s Contribution
Einstein proposed that light consists of discrete packets of energy called quanta or photons, challenging the classical wave theory of light. Each photon carries an energy proportional to its frequency ( f ), given by:
\( E = hf \)
Where:
- \( E \): Energy of the photon
- \( h \): Planck’s constant (\( 6.626 \times 10^{-34} \, \text{J·s} \))
- \( f \): Frequency of light
When light shines on a metal surface, photons transfer their energy to the electrons. If the energy is sufficient to overcome the work function (( \phi )), the electrons are ejected from the surface. The remaining energy is imparted to the electron as kinetic energy. This relationship is expressed as:
\( K.E_{\text{max}} = hf – \phi \)
Where:
- \( K.E_{\text{max}} \): Maximum kinetic energy of the ejected electrons
- \( \phi \): Work function of the metal (minimum energy required to eject an electron)
Key Predictions of Einstein’s Equation
Einstein’s theory made several predictions. First, photoemission occurs only if the light’s frequency exceeds the threshold frequency (( f_{\text{threshold}} )), where:
\( hf_{\text{threshold}} = \phi \)
In addition, the kinetic energy of ejected electrons depends linearly on the frequency of light but is independent of its intensity. Furthermore, electrons are emitted almost instantaneously after absorbing a photon if the energy condition is met. These groundbreaking predictions laid the foundation for modern quantum mechanics.
Millikan’s Experiment
Robert A. Millikan, initially skeptical of Einstein’s photon theory, conducted a series of meticulous experiments between 1914 and 1916 to test the photoelectric equation. Using advanced experimental setups, Millikan precisely measured the kinetic energy of photoelectrons as a function of the frequency of light.
Experimental Setup
Millikan’s setup included:
- A vacuum chamber containing a photosensitive metal surface
- Monochromatic light sources of varying frequencies
- A device to measure the stopping potential (\( V_{\text{stop}} \)) needed to halt the photoelectrons
The stopping potential is related to the maximum kinetic energy of the photoelectrons:
\( eV_{\text{stop}} = K.E_{\text{max}} \)
Where:
- \( e \): Charge of the electron (\( 1.602 \times 10^{-19} \, \text{C} \))
Observations
Millikan’s observations were consistent with Einstein’s predictions. First, he confirmed a linear relationship between the frequency of light and the stopping potential. Additionally, the slope of the line was equal to ( \frac{h}{e} ), allowing Millikan to calculate ( h ) with remarkable accuracy. Finally, no photoelectric emission occurred below a certain threshold frequency, regardless of light intensity. These results firmly established the validity of Einstein’s equation.
Significance of Validation
Millikan’s experimental results not only validated Einstein’s photoelectric equation but also provided strong evidence for the quantum nature of light. Furthermore, his work bridged the gap between theoretical predictions and experimental proof, marking a major milestone in modern physics.
Conclusion
Einstein’s photoelectric equation revolutionized our understanding of light and energy, laying the foundation for quantum mechanics. Millikan’s rigorous experiments confirmed the equation’s validity, solidifying the concept of photons and Planck’s constant in physics. Together, their contributions continue to inspire advancements in fields like quantum computing, photovoltaics, and spectroscopy.
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