Lecture 5

Lecture 5 - Wave-Particle Duality If electromagnetic...

Info iconThis preview shows pages 1–6. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Wave-Particle Duality If electromagnetic radiation has dual character and can be regarded as being particle-like, is it possible that matter could have wavelike properties? In 1924, Louis de Broglie made a revolutionary proposition: Small particles of matter may at times display wave-like properties . de Broglie recognized that standing waves are examples of quantization and suggested that the electron in a Bohr orbit may be associated with a circular standing wave. The Heisenberg Uncertainty Principle Heisenberg investigated this issue in detail and concluded that the wave-particle duality places a fundamental limitation on how precisely we can know the location and momentum of any object at the same instant in time: the Heisenberg Uncertainty Principle . p x h 4 p = uncertainty in momentum x = uncertainty in position This limitation only becomes important when the masses are as small as an electron, in which case the particles become "fuzzy" and cannot be localized. The Schrdinger Equation De Broglie's work showed that electrons have wave-like character and the uncertainty principle showed that detailed trajectories cannot be defined if the energy of the atom is well-defined. Schrdinger rationalized that if an electron is a wave, its position and movement in space must be described by a wave equation . For this reason, we are only going to be discussing the probability of locating an electron at a certain point in an atom. The Schrdinger Equation H = E H is the Hamiltonian operator E is the energy is the wave function . The Schrodinger equation is a differential equation and the solutions to the equation are the wavefunction and energy . For this course, we only need to know understand the nature of the solutions and not the means to obtain the solutions. itself has no physical significance (and may be positive or negative), but it contains the information to describe ALL properties of the wave. For example, 2 is the probability density for finding an electron at a given point. Solutions of the Schrdinger Equation for a Particle in a 1-Dimensional Box ZPE Note that the energy of the particle cannot be zero - this is the so-called "zero point energy" ( ZPE ) and is required by the uncertainty principle . If the energy were to be zero, the momentum would be zero and the uncertainty principle would be violated (because the uncertainty in position could not be infinite since it is somewhere in the box!). Particles in a potential well always have energy and are never at rest !...
View Full Document

Page1 / 31

Lecture 5 - Wave-Particle Duality If electromagnetic...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online