Approximating Energy Levels for a Particle in a Box
Probably one of the more startling revelations of Quantum Theory is the ‘wave-like’ nature of all particles. Not just photons. Physicists had a much easier time accepting the wavelike nature of photons (after all, light acted and behaved like a wave most of the time) than they did of other particles. De-Broglie’s hypothesis that not just photons, but electrons, protons etc. – all had a wave-like aspect about them. They could be made to interfere and bend around obstacles. The equation that described this wavelike behavior of particles – relates the momentum (a particle attribute) to the wavelength (a wave attribute):
(1)
Particle in a Potential Well (e.g. electron in an atom)
The dimension a of the box that contains the particle, must contain an integral number of wavelengths (actually ‘half-wave-lengths). If the width of the box (a) is considered to be proportional to the energy of the particle, we have an approximate equation:
which means
Leave a Reply