StudySmarter - The all-in-one study app.

4.8 • +11k Ratings

More than 3 Million Downloads

Free

Suggested languages for you:

Americas

Europe

Wave-Particle Duality

The concept of wave-particle duality says that light has properties of both a particle and a wave. It also says that small particles such as electrons behave like both waves and particles.This idea was proposed by Louis de Broglie when he outlined the results of some experiments in his PhD thesis. De Broglie’s ideas are similar to Albert Einstein’s, namely,…

Content verified by subject matter experts

Free StudySmarter App with over 20 million students

Explore our app and discover over 50 million learning materials for free.

Wave-Particle Duality

- Astrophysics
- Absolute Magnitude
- Astronomical Objects
- Astronomical Telescopes
- Black Body Radiation
- Classification by Luminosity
- Classification of Stars
- Cosmology
- Doppler Effect
- Exoplanet Detection
- Hertzsprung-Russell Diagrams
- Hubble's Law
- Large Diameter Telescopes
- Quasars
- Radio Telescopes
- Reflecting Telescopes
- Stellar Spectral Classes
- Telescopes
- Atoms and Radioactivity
- Fission and Fusion
- Medical Tracers
- Nuclear Reactors
- Radiotherapy
- Random Nature of Radioactive Decay
- Thickness Monitoring
- Circular Motion and Gravitation
- Applications of Circular Motion
- Centripetal and Centrifugal Force
- Circular Motion and Free-Body Diagrams
- Fundamental Forces
- Gravitational and Electric Forces
- Gravity on Different Planets
- Inertial and Gravitational Mass
- Vector Fields
- Conservation of Energy and Momentum
- Dynamics
- Application of Newton's Second Law
- Buoyancy
- Drag Force
- Dynamic Systems
- Free Body Diagrams
- Normal Force
- Springs Physics
- Superposition of Forces
- Tension
- Electric Charge Field and Potential
- Charge Distribution
- Charged Particle in Uniform Electric Field
- Conservation of Charge
- Electric Field Between Two Parallel Plates
- Electric Field Lines
- Electric Field of Multiple Point Charges
- Electric Force
- Electric Potential Due to Dipole
- Electric Potential due to a Point Charge
- Electrical Systems
- Equipotential Lines
- Electricity
- Ammeter
- Attraction and Repulsion
- Basics of Electricity
- Batteries
- Capacitors in Series and Parallel
- Circuit Schematic
- Circuit Symbols
- Circuits
- Current Density
- Current-Voltage Characteristics
- DC Circuit
- Electric Current
- Electric Generators
- Electric Motor
- Electrical Power
- Electricity Generation
- Emf and Internal Resistance
- Kirchhoff's Junction Rule
- Kirchhoff's Loop Rule
- National Grid Physics
- Ohm's Law
- Potential Difference
- Power Rating
- RC Circuit
- Resistance
- Resistance and Resistivity
- Resistivity
- Resistors in Series and Parallel
- Series and Parallel Circuits
- Simple Circuit
- Static Electricity
- Superconductivity
- Time Constant of RC Circuit
- Transformer
- Voltage Divider
- Voltmeter
- Electricity and Magnetism
- Benjamin Franklin's Kite Experiment
- Changing Magnetic Field
- Circuit Analysis
- Diamagnetic Levitation
- Electric Dipole
- Electric Field Energy
- Magnets
- Oersted's Experiment
- Voltage
- Electromagnetism
- Electrostatics
- Energy Physics
- Big Energy Issues
- Conservative and Non Conservative Forces
- Efficiency in Physics
- Elastic Potential Energy
- Electrical Energy
- Energy and the Environment
- Forms of Energy
- Geothermal Energy
- Gravitational Potential Energy
- Heat Engines
- Heat Transfer Efficiency
- Kinetic Energy
- Mechanical Power
- Potential Energy
- Potential Energy and Energy Conservation
- Pulling Force
- Renewable Energy Sources
- Wind Energy
- Work Energy Principle
- Engineering Physics
- Angular Momentum
- Angular Work and Power
- Engine Cycles
- First Law of Thermodynamics
- Moment of Inertia
- Non-Flow Processes
- PV Diagrams
- Reversed Heat Engines
- Rotational Kinetic Energy
- Second Law and Engines
- Thermodynamics and Engines
- Torque and Angular Acceleration
- Famous Physicists
- Fields in Physics
- Alternating Currents
- Capacitance
- Capacitor Charge
- Capacitor Discharge
- Coulomb's Law
- Dielectric
- Electric Field Strength
- Electric Fields
- Electric Potential
- Electromagnetic Induction
- Energy Stored by a Capacitor
- Equipotential Surface
- Escape Velocity
- Gravitational Field Strength
- Gravitational Fields
- Gravitational Potential
- Magnetic Fields
- Magnetic Flux Density
- Magnetic Flux and Magnetic Flux Linkage
- Moving Charges in a Magnetic Field
- Newton’s Laws
- Operation of a Transformer
- Parallel Plate Capacitor
- Planetary Orbits
- Synchronous Orbits
- Fluids
- Absolute Pressure and Gauge Pressure
- Application of Bernoulli's Equation
- Archimedes' Principle
- Conservation of Energy in Fluids
- Fluid Flow
- Fluid Systems
- Force and Pressure
- Force
- Conservation of Momentum
- Contact Forces
- Elastic Forces
- Force and Motion
- Gravity
- Impact Forces
- Moment Physics
- Moments Levers and Gears
- Moments and Equilibrium
- Pressure
- Resultant Force
- Safety First
- Time Speed and Distance
- Velocity and Acceleration
- Work Done
- Fundamentals of Physics
- Further Mechanics and Thermal Physics
- Bottle Rocket
- Charles law
- Circular Motion
- Diesel Cycle
- Gas Laws
- Heat Transfer
- Heat Transfer Experiments
- Ideal Gas Model
- Ideal Gases
- Kinetic Theory of Gases
- Models of Gas Behaviour
- Newton's Law of Cooling
- Periodic Motion
- Rankine Cycle
- Resonance
- Simple Harmonic Motion
- Simple Harmonic Motion Energy
- Temperature
- Thermal Equilibrium
- Thermal Expansion
- Thermal Physics
- Volume
- Work in Thermodynamics
- Geometrical and Physical Optics
- Kinematics Physics
- Air Resistance
- Angular Kinematic Equations
- Average Velocity and Acceleration
- Displacement, Time and Average Velocity
- Frame of Reference
- Free Falling Object
- Kinematic Equations
- Motion in One Dimension
- Motion in Two Dimensions
- Rotational Motion
- Uniformly Accelerated Motion
- Linear Momentum
- Magnetism
- Ampere force
- Earth's Magnetic Field
- Fleming's Left Hand Rule
- Induced Potential
- Magnetic Forces and Fields
- Motor Effect
- Particles in Magnetic Fields
- Permanent and Induced Magnetism
- Magnetism and Electromagnetic Induction
- Eddy Current
- Faraday's Law
- Induced Currents
- Inductance
- LC Circuit
- Lenz's Law
- Magnetic Field of a Current-Carrying Wire
- Magnetic Flux
- Magnetic Materials
- Monopole vs Dipole
- RL Circuit
- Measurements
- Mechanics and Materials
- Acceleration Due to Gravity
- Bouncing Ball Example
- Bulk Properties of Solids
- Centre of Mass
- Collisions and Momentum Conservation
- Conservation of Energy
- Density
- Elastic Collisions
- Force Energy
- Friction
- Graphs of Motion
- Linear Motion
- Materials
- Materials Energy
- Moments
- Momentum
- Power and Efficiency
- Projectile Motion
- Scalar and Vector
- Terminal Velocity
- Vector Problems
- Work and Energy
- Young's Modulus
- Medical Physics
- Absorption of X-Rays
- CT Scanners
- Defects of Vision
- Defects of Vision and Their Correction
- Diagnostic X-Rays
- Effective Half Life
- Electrocardiography
- Fibre Optics and Endoscopy
- Gamma Camera
- Hearing Defects
- High Energy X-Rays
- Lenses
- Magnetic Resonance Imaging
- Noise Sensitivity
- Non Ionising Imaging
- Physics of Vision
- Physics of the Ear
- Physics of the Eye
- Radioactive Implants
- Radionuclide Imaging Techniques
- Radionuclide Imaging and Therapy
- Structure of the Ear
- Ultrasound Imaging
- X-Ray Image Processing
- X-Ray Imaging
- Modern Physics
- Bohr Model of the Atom
- Disintegration Energy
- Franck Hertz Experiment
- Mass Energy Equivalence
- Nuclear Reaction
- Nucleus Structure
- Quantization of Energy
- Spectral Lines
- The Discovery of the Atom
- Wave Function
- Nuclear Physics
- Alpha Beta and Gamma Radiation
- Binding Energy
- Half Life
- Induced Fission
- Mass and Energy
- Nuclear Instability
- Nuclear Radius
- Radioactive Decay
- Radioactivity
- Rutherford Scattering
- Safety of Nuclear Reactors
- Oscillations
- Energy Time Graph
- Energy in Simple Harmonic Motion
- Hooke's Law
- Kinetic Energy in Simple Harmonic Motion
- Mechanical Energy in Simple Harmonic Motion
- Pendulum
- Period of Pendulum
- Period, Frequency and Amplitude
- Phase Angle
- Physical Pendulum
- Restoring Force
- Simple Pendulum
- Spring-Block Oscillator
- Torsional Pendulum
- Velocity
- Particle Model of Matter
- Physical Quantities and Units
- Converting Units
- Physical Quantities
- SI Prefixes
- Standard Form Physics
- Units Physics
- Use of SI Units
- Physics of Motion
- Acceleration
- Angular Acceleration
- Angular Displacement
- Angular Velocity
- Centrifugal Force
- Centripetal Force
- Displacement
- Equilibrium
- Forces of Nature Physics
- Galileo's Leaning Tower of Pisa Experiment
- Inclined Plane
- Inertia
- Mass in Physics
- Speed Physics
- Static Equilibrium
- Radiation
- Antiparticles
- Antiquark
- Atomic Model
- Classification of Particles
- Collisions of Electrons with Atoms
- Conservation Laws
- Electromagnetic Radiation and Quantum Phenomena
- Isotopes
- Neutron Number
- Particles
- Photons
- Protons
- Quark Physics
- Specific Charge
- The Photoelectric Effect
- Wave-Particle Duality
- Rotational Dynamics
- Angular Impulse
- Angular Kinematics
- Angular Motion and Linear Motion
- Connecting Linear and Rotational Motion
- Orbital Trajectory
- Rotational Equilibrium
- Rotational Inertia
- Satellite Orbits
- Third Law of Kepler
- Scientific Method Physics
- Data Collection
- Data Representation
- Drawing Conclusions
- Equations in Physics
- Uncertainties and Evaluations
- Space Physics
- Thermodynamics
- Heat Radiation
- Thermal Conductivity
- Thermal Efficiency
- Thermodynamic Diagram
- Thermodynamic Force
- Thermodynamic and Kinetic Control
- Torque and Rotational Motion
- Centripetal Acceleration and Centripetal Force
- Conservation of Angular Momentum
- Force and Torque
- Muscle Torque
- Newton's Second Law in Angular Form
- Simple Machines
- Unbalanced Torque
- Translational Dynamics
- Centripetal Force and Velocity
- Critical Speed
- Free Fall and Terminal Velocity
- Gravitational Acceleration
- Kinetic Friction
- Object in Equilibrium
- Orbital Period
- Resistive Force
- Spring Force
- Static Friction
- Turning Points in Physics
- Cathode Rays
- Discovery of the Electron
- Einstein's Theory of Special Relativity
- Electromagnetic Waves
- Electron Microscopes
- Electron Specific Charge
- Length Contraction
- Michelson-Morley Experiment
- Millikan's Experiment
- Newton's and Huygens' Theories of Light
- Photoelectricity
- Relativistic Mass and Energy
- Special Relativity
- Thermionic Electron Emission
- Time Dilation
- Wave Particle Duality of Light
- Waves Physics
- Acoustics
- Applications of Ultrasound
- Applications of Waves
- Diffraction
- Diffraction Gratings
- Doppler Effect in Light
- Earthquake Shock Waves
- Echolocation
- Image Formation by Lenses
- Interference
- Light
- Longitudinal Wave
- Longitudinal and Transverse Waves
- Mirror
- Oscilloscope
- Phase Difference
- Polarisation
- Progressive Waves
- Properties of Waves
- Ray Diagrams
- Ray Tracing Mirrors
- Reflection
- Refraction
- Refraction at a Plane Surface
- Resonance in Sound Waves
- Seismic Waves
- Snell's law
- Spectral Colour
- Standing Waves
- Stationary Waves
- Total Internal Reflection in Optical Fibre
- Transverse Wave
- Ultrasound
- Wave Characteristics
- Wave Speed
- Waves in Communication
- X-rays
- Work Energy and Power
- Conservative Forces and Potential Energy
- Dissipative Force
- Energy Dissipation
- Energy in Pendulum
- Force and Potential Energy
- Force vs. Position Graph
- Orbiting Objects
- Potential Energy Graphs and Motion
- Spring Potential Energy
- Total Mechanical Energy
- Translational Kinetic Energy
- Work Energy Theorem
- Work and Kinetic Energy

Save the explanation now and read when you’ve got time to spare.

SaveLerne mit deinen Freunden und bleibe auf dem richtigen Kurs mit deinen persönlichen Lernstatistiken

Jetzt kostenlos anmeldenNie wieder prokastinieren mit unseren Lernerinnerungen.

Jetzt kostenlos anmeldenThe concept of wave-particle duality says that light has properties of both a particle and a wave. It also says that small particles such as electrons behave like both waves and particles.

This idea was proposed by Louis de Broglie when he outlined the results of some experiments in his PhD thesis. De Broglie’s ideas are similar to Albert Einstein’s, namely, that light, which was assumed to be a wave, could also be described as a particle with a fixed energy called ‘**quantum**’.

Light was considered to be propagating as waves until the early 20th century. Only 25 years before de Broglie found that particles had wave-like behaviour, Einstein had studied the photoelectric effect, assuming that light was composed of a small stream of particles with an energy equal to its **frequency** f and the **Planck constant** h. This revolutionised our understanding of light, which now could also be described as a particle.

At the beginning of the 19th century, scientists believed light to be a particle. Even concepts, such as the vacuum and light being part of the electromagnetic spectrum, had not yet been established. The concepts of light having the properties of both a particle and a wave, and of small particles having the properties of light, led to several important developments:

**Thomas Young**demonstrated how light is a wave phenomenon.**Albert Einstein**proposed that light is composed of small particles called quanta.**Louis de Broglie**developed a theory explaining that small particles have wave-like properties.**Clinton Davisson**,**Paget Thomson**,**Lester Germer**conducted experiments on electron diffraction patterns.

In the beginning, it was proposed that light is composed of small particles travelling in space. This theory tried to explain light as particles travelling through a medium that filled the universe and was named aether.

However, the corpuscular theory of light being small objects was not able to explain all the properties of light, such as how waves reduced their speed and changed their direction when entering water if they were not travelling through the water. An important argument against the corpuscular theory was this inability to explain the diffraction of light.

Light’s diffraction could not be explained by the corpuscular theory. During light refraction, light particles enter a small gap and should pass through as a single beam. However, particles spread in a phenomenon known as diffraction, just as ocean waves pass through a bay

Experiments conducted by British scientist Thomas Young provided a new perception of light. The experiments were simple but also very smart. Passing a ray of light through a small aperture in a series of plates, he observed patterns of wave-like behaviour.

If light was a particle, it could simply pass through and would show over the open slits. If, however, light was a wave, it would spread after the slits, showing a pattern of interference. Young obtained an **interference pattern**, which confirmed that light behaved like a wave.

Thomas Young’s experiment demonstrated patterns of interference. Light behaves like a wave because, after passing through the small apertures, ‘diffraction’ causes some areas (red) to amplify and others (green) to nullify. This is similar to the behaviour of ocean waves, where two crests amplify each other while a crest and valley nullify each other

Einstein proposed that light consists of small particles and that its energy depends on its frequency.

His ideas developed in connection with his work on the photoelectric effect. It was expected that more intense light would make the electrons jump more, but this did not happen. Only when the frequency of the light was increased did the electrons jump from the metallic plate.

Einstein, therefore, proposed that it was the energy of a particle called quantum that was impacting the metal plate and that it was this that was responsible for ejecting the electrons from the plate.

Having described how electrons disperse after impacting a crystal, de Broglie developed a theory in which he proposed that light behaves as both a wave and a particle. He found that the dispersion of the electrons presented a wave-like pattern and proposed a formula that connects the velocity and mass of particles with their wavelength.

Clinton Davisson, Paget Thomson, and Lester Germer conducted experiments in which they fired electrons onto a crystal. The electrons did not collide against the crystal but rather passed through the material, showing a wave-like pattern after the impact.

These diffraction experiments conducted by Davisson and others were the final confirmation that electrons can behave like a wave.

Diffraction experiments with electron beams confirmed wave-particle duality. Particles passed through two slits, and the impacts were recorded on a plate. An interference pattern was found, demonstrating that electrons can behave like waves

De Broglie concluded that if electrons could behave like waves, particles had a wavelength. He linked the energy of the wavelength of the light particles to the energy of a particle moving with a certain kinetic energy. This tells us that the photon energy must be the energy given to the particle to put it into motion.

In the case of light that can be seen as an electromagnetic wave, its energy is inversely proportional to its wavelength, with smaller wavelengths having larger amounts of energy. In the calculation below, λ is the photon’s wavelength in metres, while h and c are the Planck constant and light’s velocity in a vacuum, with the following values:

\(h = 6.63 \cdot 10^{-34} m^2 kg/s = 3 \cdot 10^8 m/s\)

\[E_{photon} = \frac{h \cdot c}{\lambda}\]

Einstein derived a relationship between the energy of a particle and its mass ‘m’ given in kilograms. E is the energy given in joules, and c is the light’s velocity in a vacuum.

\[E_{particle} = m c^2\]

This says that the mass of a particle at rest has an energy equivalence.

We can simply say that the energies of both a particle and a photon are the same.

\[E_{particle} = E_{photon}\]

The mass is m, the particle velocity is v, the wavelength of the photon impacting the particle is λ, and h and c* *are the Planck constant and the velocity of light in a vacuum.

\[\frac{h \cdot c}{\lambda} = m c^2\]

To obtain the related wavelength of the particle, we equate both formulas and solve for the wavelength λ.

\[\frac{h \cdot c}{m c^2} = \lambda \]

Reducing this, we get:

\[\frac{h}{mc} = \lambda\]

Here, c can be exchanged with v, which is the proper velocity of the moving particle.

\[\frac{h}{mc} = \lambda\]

This wavelength is known as d**e ****Broglie’s wavelength of a particle**.

**Calculating the wavelength of a moving electron**

You have an electron moving at 10% of the speed of light and want to calculate its wavelength. You know the speed of light, the Planck constant, and the mass of the electron, which is approximately 9.1⋅10^{-31} kg.

Adding all the values, you get:

\(v = (0.1) \cdot (3 \cdot 10^8 m/s)\)

\(\lambda = \frac{6.63 \cdot 10^{-34} J/Hz}{(9.1 \cdot 10^{-31} kg)(0.1)(3 \cdot 10^8 m/s)}\)

\(\lambda = 2.43 \cdot 10^{-11} m\)

As you can see, that wavelength is very small and is inversely proportional to the electron’s momentum.

- Particles and light have properties that make them behave like both a wave and a particle at the same time.
- Particles have an associated wavelength known as ‘de Broglie’s wavelength’.
- An important experiment confirming that light is a wave was the two-slit experiment designed by Thomas Young. It was Einstein who introduced the idea of light as a small particle with a fixed amount of energy.
- Wave-particle duality was discovered experimentally by several scientists, but it was de Broglie who introduced the concept of a wavelength being associated with each particle.
- The wavelengths of particles are inversely proportional to their energies.

Yes, they do.

More about Wave-Particle Duality

How would you like to learn this content?

Creating flashcards

Studying with content from your peer

Taking a short quiz

How would you like to learn this content?

Creating flashcards

Studying with content from your peer

Taking a short quiz

Free physics cheat sheet!

Everything you need to know on . A perfect summary so you can easily remember everything.

Be perfectly prepared on time with an individual plan.

Test your knowledge with gamified quizzes.

Create and find flashcards in record time.

Create beautiful notes faster than ever before.

Have all your study materials in one place.

Upload unlimited documents and save them online.

Identify your study strength and weaknesses.

Set individual study goals and earn points reaching them.

Stop procrastinating with our study reminders.

Earn points, unlock badges and level up while studying.

Create flashcards in notes completely automatically.

Create the most beautiful study materials using our templates.

Sign up to highlight and take notes. It’s 100% free.

Save explanations to your personalised space and access them anytime, anywhere!

Sign up with Email Sign up with AppleBy signing up, you agree to the Terms and Conditions and the Privacy Policy of StudySmarter.

Already have an account? Log in