Question

What are matter waves? Explain. Write the formula for de Broglie wavelength. Write the name of the experiment which shows the dual nature of particles.

Hint:

Wave-particle duality shows that particles such as electrons can exhibit both wave-like properties, such as interference and diffraction, and particle-like properties, such as momentum and energy.

Answer 1

Matter Waves:
Matter waves, also called de Broglie waves, are the waves associated with particles that exhibit both wave-like and particle-like properties. According to de Broglie’s hypothesis, every moving particle, such as an electron or a proton, behaves like a wave and has an associated wavelength. This concept was proposed by Louis de Broglie in 1924 and is known as wave-particle duality. The de Broglie wavelength \(\lambda\) of a particle with momentum \(p\) is given by the following formula: \[ \lambda = \frac{h}{p} \] where: - \(h\) is Planck’s constant (\(h = 6.626 \times 10^{-34} \ \mathrm{J . s}\)), - \(p\) is the momentum of the particle (\(p = mv\), where \(m\) is the mass and \(v\) is the velocity of the particle). Dual Nature of Particles:
The concept of wave-particle duality was experimentally verified by the Davisson-Germer experiment, which demonstrated that electrons exhibit diffraction patterns, similar to light waves, when passed through a crystal lattice. Final Answer: The formula for de Broglie wavelength is: \[ \lambda = \frac{h}{p}. \] The experiment that shows the dual nature of particles is the Davisson-Germer experiment.