Wave –Particle Dualism of Light

The Wave Nature of Matter

Problem 1

Experimental Evidence for the Wavelike Behavior of Matter The first experiments to confirm de Broglie's hypothesis about the wavelike aspects of matter were carried out in 1927 by Clinton J. Davisson and Lester H. Germer, and independently by George Paget Thomson. They found that certain scattering directions are preferred when electrons are scattered by a crystal, a behavior typical of the scattering of a wave from a regular array such as a crystal.

Davisson-Germer Experiment

Problem 2 At what angles do diffraction peaks occur for electrons of kinetic energy 120 eV incident on a crystal whose scattering planes are 0.12 nm apart?

The diffraction of neutrons

Double-slit interference experiment A double-slit interference pattern created with electrons

De Broglie Waves and Quantum States De Broglie connected the stationary state in atoms with a standing wave and obtained the quantization condition of angular momentum very naturally. In order to let the rotation of the electron around the nucleus exist in a steady state, the wave corresponding to the electron must be a standing wave. That is, the phase of the wave must not change after one circle (Fig.), otherwise the electron wave will be destroyed.

De Broglie Waves and Quantum States

A Particle in a Rigid Box

Conclusions A bound wave yields quantization conditions. Connecting a wave with a particle cannot be understood by classical physics and can only be explained by quantum mechanics.

Problem 3 What is the quantum number of this particle confined in a box?

Problem 4 What is the quantum number of an electron confined in a 3,0-nm-long one-dimensional box if the electrons de Broglie wavelength is 1,0 nm?

Problem 5 What is the length of a one-dimensional box in which an electron in the n=1 state has the same energy as a photon with wavelength of 600 nm?