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VCE Physics Unit 4 AOS 1
Wave-Particle Duality
At the turn of the 20th century, physics was rocked by a profound dilemma. Light, which for a century seemed definitively a **wave**, suddenly started behaving like a **particle**. Stranger still, matter—the very essence of particles—began exhibiting wave-like properties. This guide explores this central conflict and the two great revolutions it spawned: Quantum Mechanics and Special Relativity.
🌊
The Wave
Exhibits interference and diffraction. Energy is spread out and continuous.
粒子
The Particle
Has momentum and a definite position. Energy is localised and discrete.
The Wave Model of Light
The classical model describes light as a transverse electromagnetic wave. Evidence like diffraction and interference strongly supports this view. Young’s double-slit experiment is the definitive proof, showing that light waves interfere to create a pattern of bright and dark fringes.
Young’s Double-Slit Experiment
Use the sliders to see how wavelength ($\lambda$), slit separation ($d$), and screen distance ($L$) affect the interference pattern.
Calculated Fringe Spacing ($\Delta x$): 2.20 mm
The Photoelectric Effect
The classical wave theory couldn’t explain why light ejects electrons from a metal only above a certain frequency. Einstein’s solution was the **photon**: a particle of light. This interactive shows how a photon’s energy ($hf$) must overcome the metal’s work function ($\Phi$) to release an electron with kinetic energy.
Work Function ($\Phi$): …
Threshold Frequency ($f_0$): …
Selected Frequency ($f$): …
Max Kinetic Energy ($E_{k(max)}$): …
The Wave Nature of Matter
If waves can be particles, could particles be waves? Louis de Broglie thought so, proposing that all matter has a wavelength ($\lambda = h/p$). This was confirmed by electron diffraction, proving that electrons behave like waves. This concept also explains why atomic energy levels are quantised: they are simply electron standing waves.
Electron Standing Waves
An electron’s orbit is stable only if its circumference allows a standing wave to form. Adjust ‘n’ to see how only integer values create a stable pattern.
De Broglie Wavelength
This calculator shows why wave effects are negligible for large objects but significant for electrons. Select an object and set its speed.
Momentum (p): …
Wavelength ($\lambda$): …
Einstein’s Special Relativity
Based on the simple idea that the speed of light is constant for everyone, Einstein revolutionized physics. His theory shows that moving clocks run slow (time dilation) and moving objects shrink (length contraction). Use the slider to see these bizarre effects become significant as you approach the speed of light.
Lorentz Factor ($\gamma$)
1.000
Time Dilation
1 year for you is…
1.00 years
…on Earth
Length Contraction
A 100m spaceship appears…
100.0 m
…long
Mass and Energy
Perhaps the most profound outcome of relativity is the discovery that mass is a form of energy. The equation $E_0=m_0c^2$ shows that a small amount of mass can be converted into a huge amount of energy. This principle powers stars and nuclear reactions. An object’s kinetic energy is the extra energy it gains from motion.
Relativistic Energy Calculator
Observe how an object’s kinetic energy increases non-linearly and approaches infinity as its velocity nears the speed of light.
Rest Energy ($E_0$)
The intrinsic energy of mass.
Kinetic Energy ($E_k$)
0.00 x E₀
…as a multiple of rest energy.
