De-Broglie hypothesized that material particles have wave like properties. Figure shows a small
Channel: Doubtnut
Date: 12/04/2020

De-Broglie hypothesized that material particles have wave like properties. Figure shows a small particle in a box. The particle simply bounces back and forth at constant speed. As particles also have wave like properties it can be considered to be a wave reflecting back and forth from the ends of the box. The reflections will create a standing wave analogous to standing wave on a string tied at both ends. Since a standing wave confined to a region can have only selected wavelength, momentum of the particle is quantized. We can safely assume that such a particle only has kinetic energy. This energy must also be quantized.   What is momentum of particle in n^(th) mode of standing wave ?