Dual Nature of Light

• Light exhibits both wave nature and particle nature.
• Wave nature is observed in:
  • Interference
  • Diffraction
  • Polarisation
• Particle nature is observed in:
  • Photoelectric effect
  • Compton effect

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de Broglie Hypothesis

• In 1924, French physicist Louis de Broglie proposed that moving material particles also possess wave nature.
• According to him, if light (energy) shows dual nature, then matter should also exhibit dual nature.

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de Broglie Wavelength

The wavelength associated with a moving particle is called the de Broglie wavelength.

Formula

$$\boxed{\lambda=\frac{h}{p}}$$

Since,$$p=mv$$

therefore,$$\boxed{\lambda=\frac{h}{mv}}$$

where:

• $\lambda$ = de Broglie wavelength
• $h$ = Planck’s constant $(6.626 \times 10^{-34}\,\text{J s})$(6.626×10−34J s)
• $p$ = Momentum of particle
• $m$ = Mass of particle
• $v$= Velocity of particle

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Significance of de Broglie Equation

• It establishes the dual nature of matter.
• The left side ($\lambda$λ) represents the wave property.
• The right side ($mv$mv) represents the particle property.

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de Broglie Wavelength of a Photon

For a photon,$$p=\frac{h\nu}{c}$$

Substituting in the de Broglie equation,$$\lambda=\frac{h}{p} =\frac{hc}{h\nu} =\frac{c}{\nu}$$

Since,$$\boxed{\lambda=\frac{c}{\nu}}$$

Thus, the de Broglie wavelength of a photon is the same as the wavelength of electromagnetic radiation.

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Dependence of de Broglie Wavelength

From$$\lambda=\frac{h}{mv}$$

• Mass increases → Wavelength decreases
• Velocity increases → Wavelength decreases

Thus,

• Heavy particles have very small de Broglie wavelength.
• Light particles have larger de Broglie wavelength.

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Why Don’t We Observe Wave Nature of Everyday Objects?

• Macroscopic objects have very large mass, so their de Broglie wavelength is extremely small.
• Such small wavelengths cannot be detected experimentally.
• Therefore, everyday objects do not show observable wave nature.

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Wave Nature of Microscopic Particles

• Electrons, protons, neutrons and other subatomic particles have small mass.
• Their de Broglie wavelength is measurable.
• Hence, they exhibit wave properties such as diffraction and interference.

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CBSE Important Points

• Proposed by Louis de Broglie (1924).
• Every moving particle has an associated matter wave.
• Matter waves are called de Broglie waves.
• De Broglie wavelength is: $$\boxed{\lambda=\frac{h}{mv}}$$
• Higher momentum → Smaller wavelength.
• Wave nature is significant only for microscopic particles.
• The de Broglie wavelength of a photon is equal to the wavelength of the corresponding electromagnetic radiation.