Dual Nature of Radiation and Matter Class 12 Physics Notes | Complete Guide 2025

The dual nature of radiation and matter is a fundamental concept in quantum physics. It reveals that light and matter exhibit both wave-like and particle-like properties. Classical physics failed to explain certain phenomena—like the photoelectric effect and Compton scattering—until this duality was introduced. Understanding this duality is essential for modern physics, as it underlies quantum mechanics, atomic structure, electronics, etc.

Dual Nature of Radiation and Matter Class 12 Physics Notes | Complete Guide 2025

1. What Is Dual Nature?

1.1 Definition

Dual nature means that entities like radiation (light) and matter do not strictly behave like only waves or only particles. Depending on the experimental setup, they sometimes show wave behaviour (such as interference, diffraction) and sometimes particle behaviour (such as discrete energy packets, collisions).

1.2 Historical Context

• Early 19th century: Light understood as wave (Young’s double slit, interference, diffraction).

• Late 19th to early 20th century: Some phenomena (black body radiation, photoelectric effect, Compton effect) defied wave-only theory.

• Planck (1900): Introduced quantization of radiation.

• Einstein (1905): Explained photoelectric effect via photons.

• de Broglie (1924): Suggested matter (electrons etc.) have wavelength.

2. Dual Nature of Radiation

2.1 Evidence of Wave Nature of Light

2.1.1 Interference

• When light from two coherent sources overlaps, there are regions of constructive and destructive interference leading to fringes (bright and dark bands).

• Example: Young’s double-slit experiment demonstrates this beautifully.

2.1.2 Diffraction

• Light bending around edges or through slits of comparable size to its wavelength produces diffraction patterns.

2.1.3 Polarization

• Light waves being transverse allows polarization (directional oscillation of electric vector). Particle model cannot easily explain polarization.

2.2 Evidence of Particle Nature of Light

2.2.1 Photoelectric Effect

• When light of certain (threshold) frequency strikes a metal surface, electrons are emitted.

• Key observations:

  • Emission without time lag (even for low intensities) if frequency is above threshold.

  • Below threshold frequency, no emission regardless of intensity.

  • Kinetic energy of emitted electrons depends on frequency, not on intensity.

• Einstein’s explanation: Light consists of quanta called photons each of energy $E=h\nu$. A photon must have at least hν0h\nu_0hν0​ to free an electron. The excess energy becomes kinetic energy.

2.2.2 Black Body Radiation

• Classical wave theory failed to explain ultraviolet catastrophe.

• Planck’s law introduced quantization: energy is emitted in discrete units of $E=nh\nu$.

2.2.3 Compton Effect

• Scattering of X-rays by free electrons shows increase in wavelength (shift depends on scattering angle) consistent with treating photons as particles with momentum $p=h/\lambda$.

3. Dual Nature of Matter

3.1 De Broglie Hypothesis

• Louis de Broglie proposed that if radiation (light) has dual nature, perhaps matter (electrons, etc.) also have wave-properties.

• De Broglie wavelength:

  λ=hp=hmv \lambda = \frac{h}{p} = \frac{h}{mv}λ=ph​=mvh​

  where $h$ = Planck’s constant, $p$ = momentum, $m$ = mass, $v$ = velocity.

3.2 Evidence for Wave Nature of Matter

3.2.1 Electron Diffraction

• When electrons are made to pass through thin crystal foils (e.g. graphite), they display diffraction patterns, similar to X-rays. This confirms their wave nature.

3.2.2 Davisson-Germer Experiment

• Electrons scattered by a nickel crystal exhibit peaks of intensity at certain angles, matching predictions of Bragg reflection treating electrons as waves.

3.3 Evidence for Particle Nature of Matter

• Matter (electrons, atoms) when interacting in collisions, behave like discrete particles.

• Mass, charge, localized impacts: e.g. electrons in cathode-ray tubes strike a screen at precise locations; electrons in detectors produce discrete signals.

4. Mathematical Formulation

4.1 Photon: Energy and Momentum

• Photon energy:

  E=hν=hcλ E = h\nu = \frac{hc}{\lambda}E=hν=λhc​

  where $c$ is the speed of light.

• Photon momentum:

  p=Ec=hλ p = \frac{E}{c} = \frac{h}{\lambda}p=cE​=λh​

4.2 De Broglie Wavelength

• For a particle of rest mass $m$ moving with velocity $v$:

  λ=hmv \lambda = \frac{h}{mv}λ=mvh​

• For relativistic particles, momentum is $p=\gamma mv$ where γ=1/1−v2/c2\gamma = 1/\sqrt{1 – v^2/c^2}γ=1/1−v2/c2​, so

  λ=hγmv \lambda = \frac{h}{\gamma mv}λ=γmvh​

4.3 Wavefunction and Probability

• In quantum mechanics, matter waves are described by wavefunctions $\psi$, whose squared magnitude ∣ψ∣2|\psi|^2∣ψ∣2 gives probability density.

• Schrödinger equation governs evolution of $\psi$. (Though this is more advanced beyond the basic duality concept.)

5. Key Experiments and Their Details

5.1 Young’s Double‐Slit Experiment with Light

• Setup: coherent light source → two narrow slits → screen.

• Observation: Alternating bright & dark fringes.

• Condition for bright fringe:

  $$d\sin \theta =n\lambda (n=0,1,2,\dots )$$

• Condition for dark fringe:

  dsin⁡θ=(n+12)λ d \sin \theta = (n + \tfrac{1}{2})\lambdadsinθ=(n+21​)λ

• Significance: Shows superposition of waves, interference pattern impossible if light were only particles.

5.2 Photoelectric Effect

• Setup: Light of frequency $\nu$ and intensity $I$ incident on metal; measure number & kinetic energy of emitted electrons.

• Observations:

  1. There is a minimum frequency ν0\nu_0ν0​ below which no electrons are emitted, regardless of intensity.

  2. Above ν0\nu_0ν0​, maximum kinetic energy of electrons increases linearly with $\nu$.

  3. Number of electrons emitted (i.e., photocurrent) is proportional to intensity (once ν>ν0\nu > \nu_0ν>ν0​), but kinetic energy is not.

  4. Emission is instantaneous when frequency above threshold; no time lag.

• Einstein’s equation:

  Kmax⁡=hν−hν0 K_{\max} = h\nu – h\nu_0Kmax​=hν−hν0​

  where Kmax⁡K_{\max}Kmax​ = maximum kinetic energy of photoelectrons.

5.3 Compton Scattering

• Setup: X-ray (or gamma) photon collides with free (or loosely bound) electron; scattered photon has lower energy (longer wavelength).

• Wavelength shift equation:

  λ′−λ=hmec(1−cos⁡θ) \lambda’ – \lambda = \frac{h}{m_e c} (1 – \cos \theta)λ′−λ=me​ch​(1−cosθ)

  where $\theta$ is scattering angle, mem_eme​ electron rest mass.

• Significance: Requires treating light as particle (photon) with momentum.

5.4 Electron Diffraction (Davisson-Germer Experiment)

• Setup: Electrons accelerated through known potential → monochromatic beam → hit crystal lattice → intensity measured at various angles.

• Observation: Intensity maxima at angles satisfying Bragg’s law:

  $$2d\sin \theta =n\lambda$$

• The experimentally measured $\lambda$ matches de Broglie’s prediction $h/p$.

6. Quantum vs Classical Contrasts

7. Implications and Applications

7.1 De Broglie Wavelength in Electron Microscope

• Electron microscopes use high-energy electrons, hence very small de Broglie wavelengths → high resolution imaging of atomic structure.

7.2 Quantum Mechanics Foundations

• Dual nature is one of the pillars justifying wavefunctions, quantization, uncertainty principle, etc.

7.3 Technologies Relying on Photoelectric Effect

• Photoelectric sensors, solar cells, photodiodes, light meters, etc. They operate based on photon absorption causing electron emission.

7.4 Compton Scattering in Astrophysics and Medical Physics

• Helps in understanding X-ray scattering, radiation shielding, diagnostic imaging (e.g. in detectors), and in astrophysical processes.

8. Limitations and Unanswered Questions

8.1 Wave-Particle Complementarity

• Bohr’s principle: Wave and particle aspects are complementary; which property shows up depends on experimental arrangement.

• You cannot observe both wave and particle nature simultaneously in the same experiment fully.

8.2 Heisenberg’s Uncertainty Principle

• Related to dual nature: there are inherent limitations in simultaneously determining certain pairs of observables (e.g., position & momentum).

• The more precisely one is known, the less precise the other can be:

  Δx Δp≥ℏ2 \Delta x\, \Delta p \ge \frac{\hbar}{2}ΔxΔp≥2ℏ​

8.3 Interpretational Questions

• What is “reality” of wavefunction? Is wavefunction physically real or just a tool to compute probabilities?

• Measurement problem: how does the act of observation “collapse” the wave-like behaviour into particle detection?

9. Key Formulae Summary

• Photon energy: E=hν=hcλE = h\nu = \frac{hc}{\lambda}E=hν=λhc​

• Photon momentum: p=hλ=Ecp = \frac{h}{\lambda} = \frac{E}{c}p=λh​=cE​

• De Broglie wavelength: λ=hp=hmv\lambda = \frac{h}{p} = \frac{h}{mv}λ=ph​=mvh​ (non-relativistic), or hγmv\frac{h}{\gamma m v}γmvh​ (relativistic)

• Photoelectric effect equation: Kmax⁡=hν−hν0K_{\max} = h\nu – h\nu_0Kmax​=hν−hν0​

• Compton shift: λ′−λ=hmec(1−cos⁡θ)\lambda’ – \lambda = \frac{h}{m_e c}(1 – \cos \theta)λ′−λ=me​ch​(1−cosθ)

10. Important Definitions

• Photon: A quantum (packet) of electromagnetic radiation with energy $h\nu$ and momentum $h/\lambda$.

• Threshold frequency (ν0\nu_0ν0​): Minimum frequency of incident light required to emit electrons from a metal in the photoelectric effect.

• Work function ($\varphi$): The minimum energy required to remove an electron from the surface of a metal: ϕ=hν0\phi = h\nu_0ϕ=hν0​.

• de Broglie wavelength: Wavelength associated with any moving particle, given by $\lambda =h/p$.

11. Common Problems / Numerical Types

While this is more about solving, note these recurring problem types:

• Calculating de Broglie wavelength for given particle speed or kinetic energy.

• Photoelectric effect: finding threshold frequency, work function, kinetic energy of electrons.

• Compton scattering: finding shift in wavelength for given photon energy and scattering angle.

• Electron diffraction: using Bragg’s law to find interplanar spacing or angle of diffraction.

12. Summary

• Dual nature is essential: light and matter are neither purely wave nor purely particle.

• Experiments (photoelectric effect, Compton effect, electron diffraction) cemented the concept.

• Quantization of energy, momentum leads to modern quantum theory.

• Complementarity and uncertainty are consequences of duality.

  Objective Question Dual Nature of Radiation and Matter

  Q1. Who proposed the concept of matter waves?

  (a) Einstein
  (b) Planck
  (c) Bohr
  (d) de Broglie

  Answer: de Broglie

  Q2. Energy of a photon is given by

  (a) $E=h\nu$
  (b) E=mc2E = mc^2E=mc2
  (c) E=hλE = \frac{h}{\lambda}E=λh​
  (d) E=12mv2E = \frac{1}{2}mv^2E=21​mv2

  Answer: $E=h\nu$

  Q3. The phenomenon that proves the wave nature of light is

  (a) Photoelectric effect
  (b) Compton effect
  (c) Interference
  (d) Black body radiation

  Answer: Interference

  Q4. The particle nature of light was confirmed by

  (a) Interference
  (b) Diffraction
  (c) Photoelectric effect
  (d) Polarization

  Answer: Photoelectric effect

  Q5. The equation for de Broglie wavelength is

  (a) $\lambda =h\nu$
  (b) λ=hp\lambda = \frac{h}{p}λ=ph​
  (c) λ=ph\lambda = \frac{p}{h}λ=hp​
  (d) $\lambda =h\times p$

  Answer: λ=hp\lambda = \frac{h}{p}λ=ph​

  Q6. The work function is defined as

  (a) Maximum kinetic energy of electrons
  (b) Minimum energy to remove an electron
  (c) Energy of photon
  (d) Energy of electron beam

  Answer: Minimum energy to remove an electron

  Q7. Compton effect deals with

  (a) Scattering of gamma rays
  (b) Scattering of X-rays
  (c) Reflection of UV light
  (d) Absorption of microwaves

  Answer: Scattering of X-rays

  Q8. The Davisson-Germer experiment proved

  (a) Particle nature of light
  (b) Wave nature of electrons
  (c) Existence of positrons
  (d) Existence of neutrinos

  Answer: Wave nature of electrons

  Q9. The energy quantum is called

  (a) Electron
  (b) Photon
  (c) Neutron
  (d) Proton

  Answer: Photon

  Q10. The unit of Planck’s constant $h$ is

  (a) Joule
  (b) Joule-second
  (c) Newton
  (d) eV

  Answer: Joule-second

  Q11. The relation between kinetic energy and stopping potential is

  (a) Kmax=eV0K_{max} = eV_0Kmax​=eV0​
  (b) Kmax=V0K_{max} = V_0Kmax​=V0​
  (c) Kmax=e/hK_{max} = e/hKmax​=e/h
  (d) Kmax=eIK_{max} = eIKmax​=eI

  Answer: Kmax=eV0K_{max} = eV_0Kmax​=eV0​

  Q12. The wavelength of an electron accelerated by potential V is given by

  (a) λ=h2meV\lambda = \frac{h}{\sqrt{2meV}}λ=2meV​h​
  (b) λ=hV\lambda = \frac{h}{V}λ=Vh​
  (c) $\lambda =hV$
  (d) λ=2meV\lambda = \sqrt{2meV}λ=2meV​

  Answer: λ=h2meV\lambda = \frac{h}{\sqrt{2meV}}λ=2meV​h​

  Q13. The photon momentum is expressed as

  (a) p=Ecp = \frac{E}{c}p=cE​
  (b) $p=Ec$
  (c) p=cEp = \frac{c}{E}p=Ec​
  (d) p=E2/cp = E^2/cp=E2/c

  Answer: p=Ecp = \frac{E}{c}p=cE​

  Q14. The threshold frequency is related to

  (a) Work function
  (b) Kinetic energy
  (c) de Broglie wavelength
  (d) Photon momentum

  Answer: Work function

  Q15. Electrons show diffraction when

  (a) Moving fast
  (b) Moving slow
  (c) Passing through crystal lattice
  (d) Absorbing energy

  Answer: Passing through crystal lattice

  Q16. Photoelectric effect cannot be explained by

  

  (a) Particle nature of light
  (b) Wave nature of light
  (c) Quantum theory
  (d) Einstein’s equation

  Answer: Wave nature of light

  Q17. The Planck’s constant value is approximately

  (a) 6.63×10−34Js6.63 \times 10^{-34} Js6.63×10−34Js
  (b) 9.11×10−31Js9.11 \times 10^{-31} Js9.11×10−31Js
  (c) 3×108Js3 \times 10^8 Js3×108Js
  (d) 1.6×10−19Js1.6 \times 10^{-19} Js1.6×10−19Js

  Answer: 6.63×10−34Js6.63 \times 10^{-34} Js6.63×10−34Js

  Q18. When wavelength increases, photon energy

  (a) Increases
  (b) Decreases
  (c) Remains same
  (d) Doubles

  Answer: Decreases

  Q19. The wave associated with matter particles is called

  (a) Photon wave
  (b) Electron wave
  (c) Matter wave
  (d) Neutron wave

  Answer: Matter wave

  Q20. The kinetic energy of photoelectrons is maximum when

  (a) Frequency > Threshold frequency
  (b) Frequency < Threshold frequency
  (c) Frequency = Threshold frequency
  (d) Intensity is zero

  Answer: Frequency > Threshold frequency

  Questions And Answer Dual Nature of Radiation and Matter

  Q1. Define photoelectric effect.

  The photoelectric effect is the phenomenon in which electrons are emitted from a metal surface when light of suitable frequency falls on it.

  Q2. Who proposed the concept of matter waves?

  The concept of matter waves was proposed by Louis de Broglie in 1924.

  Q3. Write the expression for de Broglie wavelength.

  The de Broglie wavelength is given by λ=hp=hmv\lambda = \frac{h}{p} = \frac{h}{mv}λ=ph​=mvh​, where $h$ is Planck’s constant, $m$ is the mass of the particle, and $v$ is its velocity.

  Q4. What is threshold frequency in the photoelectric effect?

  Threshold frequency is the minimum frequency of incident light below which no electrons are emitted from the metal surface, regardless of the light intensity.

  Q5. Explain the wave nature of light with one example.

  The wave nature of light is proved by interference, where two coherent light sources overlap to produce alternate bright and dark fringes, as demonstrated in Young’s Double Slit Experiment.

  Q6. Explain the particle nature of light with one experiment.

  The photoelectric effect proves the particle nature of light. When photons strike a metal surface, they transfer energy to electrons, which are then emitted if the photon energy exceeds the metal’s work function.

  Q7. Write Einstein’s photoelectric equation.

  Einstein’s equation is Kmax=hν−hν0K_{max} = h\nu – h\nu_0Kmax​=hν−hν0​, where KmaxK_{max}Kmax​ is the maximum kinetic energy of electrons, $\nu$ is the frequency of incident light, and ν0\nu_0ν0​ is the threshold frequency.

  Q8. What is Planck’s quantum hypothesis?

  Planck proposed that energy is emitted or absorbed in discrete packets called quanta (photons), each having energy $E=h\nu$, where $h$ is Planck’s constant and $\nu$ is the frequency.

  Q9. State the significance of Davisson-Germer experiment.

  The Davisson-Germer experiment proved the wave nature of electrons by showing electron diffraction patterns when electrons were scattered by a crystal lattice.

  Q10. What is Compton effect?

  The Compton effect is the increase in wavelength of X-rays when they are scattered by free electrons, explained by treating light as particles (photons) with momentum.

  Q11. Derive the expression for de Broglie wavelength of a moving particle.

  For a particle with momentum $p=mv$, de Broglie proposed λ=hp\lambda = \frac{h}{p}λ=ph​.
  If the kinetic energy K=12mv2K = \frac{1}{2}mv^2K=21​mv2, then v=2Kmv = \sqrt{\frac{2K}{m}}v=m2K​​. Substituting in the above expression:

  λ=h2mK\lambda = \frac{h}{\sqrt{2mK}}λ=2mK​h​

  Q12. What are the applications of the photoelectric effect?

  Applications include:

  • Photoelectric cells for light detection.

  • Solar cells for electricity generation.

  • Automatic street lighting.

  • Photomultipliers in scientific instruments.

  Q13. Explain black body radiation in brief.

  Black body radiation refers to the electromagnetic radiation emitted by an ideal black body that absorbs all incident radiation. Classical physics failed to explain its spectrum, leading to Planck’s quantum theory.

  Q14. Give the experimental proof of wave nature of electrons.

  The Davisson-Germer experiment provided proof by showing electron diffraction patterns when accelerated electrons hit a nickel crystal, consistent with de Broglie wavelength predictions.

  Q15. State the main postulates of de Broglie hypothesis.

  1. Every moving particle is associated with a wave called a matter wave.

  2. The wavelength $\lambda$ is inversely proportional to the momentum $p$.

  3. The wave nature becomes significant only for microscopic particles.

  Q16. What is the relation between work function and threshold frequency?

  The work function $\varphi$ and threshold frequency ν0\nu_0ν0​ are related by ϕ=hν0\phi = h\nu_0ϕ=hν0​, where $h$ is Planck’s constant.

  Q17. Define photon momentum and give its formula.

  Photon momentum $p$ is given by p=hλ=Ecp = \frac{h}{\lambda} = \frac{E}{c}p=λh​=cE​, where $E$ is the energy of the photon, $\lambda$ is its wavelength, and $c$ is the speed of light.

  Q18. Explain the concept of wave-particle duality.

  Wave-particle duality means that light and matter exhibit both wave-like and particle-like properties depending on the experimental conditions, forming the foundation of quantum mechanics.

  Q19. How does the intensity of light affect photoelectric current?

  Above the threshold frequency, increasing light intensity increases the number of photons striking the metal, thus increasing the photoelectric current.

  Q20. Why can’t the photoelectric effect be explained by wave theory?

  Wave theory predicts continuous energy transfer, but experimentally, electrons are emitted instantly when photon energy exceeds the work function, proving that energy transfer is quantized.

  Subscribe My Youtube channel Class 12 Physics Wave Optics Notes | Detailed Explanation, Formulas & Questions