Question

Explain how the dual aspect of matter is evident in the de Broglie relation.

Hint:

The de Broglie relation is the bridge between wave and particle concepts: \[ \lambda=\frac{h}{p} \] Wavelength \(\rightarrow\) Wave Nature Momentum \(\rightarrow\) Particle Nature

Answer 1

Concept: One of the most revolutionary developments in modern physics was the discovery that matter exhibits both particle nature and wave nature. This idea was proposed by Louis de Broglie in 1924. According to de Broglie, every moving material particle is associated with a wave known as the matter wave or de Broglie wave.

Step 1: State the de Broglie hypothesis. De Broglie proposed that every moving particle possesses an associated wavelength called the de Broglie wavelength. The de Broglie relation is \[ \lambda=\frac{h}{p} \] where \[ \lambda \] is the de Broglie wavelength, \[ h \] is Planck's constant and \[ p \] is the momentum of the particle.

Step 2: Identify the particle aspect in the relation. The quantity \[ p=mv \] represents momentum. Momentum is a characteristic property of particles. A particle possesses mass, momentum and energy. Therefore, the appearance of momentum in the de Broglie relation indicates the particle nature of matter.

Step 3: Identify the wave aspect in the relation. The quantity \[ \lambda \] represents wavelength. Wavelength is a characteristic property of waves. Phenomena such as interference, diffraction and superposition are associated with waves. Therefore, the appearance of wavelength in the relation indicates the wave nature of matter.

Step 4: Explain the dual aspect. The de Broglie equation connects a wave quantity \((\lambda)\) with a particle quantity \((p)\). Thus, a single relation simultaneously contains both wave and particle characteristics. This demonstrates that matter cannot be described exclusively as a particle or exclusively as a wave. Instead, matter possesses a dual nature.

Step 5: Experimental verification. The wave nature predicted by de Broglie was later verified experimentally through electron diffraction experiments conducted by Davisson and Germer. The observation of diffraction of electrons confirmed that particles can exhibit wave behaviour. Final Answer: The de Broglie relation \[ \lambda=\frac{h}{p} \] connects wavelength, which is a wave property, with momentum, which is a particle property. Thus, it clearly establishes the dual nature of matter and shows that every moving particle possesses an associated wave character.