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Quantum Mechanics: A Beginner’s Guide to A-Level Science
What Is Quantum Mechanics?
Quantum mechanics studies the behavior of particles at very small scales, where classical physics no longer applies.
Key Principles of Quantum Mechanics
Wave-Particle Duality
Particles, such as electrons, exhibit both wave-like and particle-like properties.
Example: The double-slit experiment demonstrates that electrons can create an interference pattern, behaving like waves.
The Photoelectric Effect
Light can eject electrons from a metal surface if its frequency exceeds a certain threshold.
Einstein’s Equation:
![\[ E = hf \]](https://www.on22.com/wp-content/ql-cache/quicklatex.com-c7528b3a4f027a35c3b419ab61cb0ab7_l3.png "Rendered by QuickLaTeX.com")
Where:
![E]( "Rendered by QuickLaTeX.com")
: Energy of a photon (J)![h = 6.63 \times 10^{-34} \, \text{J·s}]( "Rendered by QuickLaTeX.com")
: Planck’s constant![f]( "Rendered by QuickLaTeX.com")
: Frequency (Hz)
: Energy of a photon (J)
: Planck’s constant
: Frequency (Hz)Heisenberg’s Uncertainty Principle
It is impossible to simultaneously measure the exact position and momentum of a particle:
![\[ \Delta x \cdot \Delta p \geq \frac{h}{4\pi} \]](https://www.on22.com/wp-content/ql-cache/quicklatex.com-6867f23360267326c7699f313efe2c2b_l3.png "Rendered by QuickLaTeX.com")
Applications of Quantum Mechanics
- Semiconductors: Powering computers and smartphones
- Medical Imaging: MRI technology
- Quantum Computing: Revolutionizing computation with qubits
Example Problem
Light with a wavelength of 
strikes a metal with a work function of 
. Determine if electrons are ejected.
- Photon Energy:
![\[ E = \frac{hc}{\lambda} = \frac{(6.63 \times 10^{-34})(3.0 \times 10^8)}{400 \times 10^{-9}} = 4.97 \times 10^{-19} \, \text{J} = 3.1 \, \text{eV} \]]( "Rendered by QuickLaTeX.com")
- Since
![E > 2 \, \text{eV}]( "Rendered by QuickLaTeX.com")
, electrons are ejected.
![\[ E = \frac{hc}{\lambda} = \frac{(6.63 \times 10^{-34})(3.0 \times 10^8)}{400 \times 10^{-9}} = 4.97 \times 10^{-19} \, \text{J} = 3.1 \, \text{eV} \]](https://www.on22.com/wp-content/ql-cache/quicklatex.com-e1f3307c027464a7980861c275dca93e_l3.png "Rendered by QuickLaTeX.com")
, electrons are ejected.Common Mistakes in Quantum Mechanics
- Forgetting to convert units (e.g., nm to m)
- Mixing up photon energy and threshold energy
- Misinterpreting wave-particle duality
Practice Questions
- Calculate the energy of a photon with a wavelength of
![500 \, \text{nm}]( "Rendered by QuickLaTeX.com")
. - Explain the significance of the photoelectric effect in quantum theory.
- Describe one application of wave-particle duality.
.
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