de Broglie wavelength

Examples of de Broglie wavelength in the following topics:

• The de Broglie Wavelength

  • The de Broglie wavelength is inversely proportional to the momentum of a particle.
  • When the de Broglie wavelength was inserted into the Bragg condition, the observed diffraction pattern was predicted, thereby experimentally confirming the de Broglie hypothesis for electrons.
  • At these temperatures, the thermal de Broglie wavelengths come into the micrometer range.
  • The researchers calculated a de Broglie wavelength of the most probable C60 velocity as 2.5 pm.
  • Use the de Broglie equations to determine the wavelength, momentum, frequency, or kinetic energy of particles

• de Broglie and the Wave Nature of Matter

  • The concept of "matter waves" or "de Broglie waves" reflects the wave-particle duality of matter.
  • The theory was proposed by Louis de Broglie in 1924 in his PhD thesis.
  • The de Broglie relations show that the wavelength is inversely proportional to the momentum of a particle, and is also called de Broglie wavelength.
  • De Broglie didn't have any experimental proof at the time of his proposal.
  • The researchers calculated a De Broglie wavelength of the most probable C60 velocity as 2.5 pm.

• Diffraction Revisited

  • De Broglie's hypothesis was that particles should show wave-like properties such as diffraction or interference.
  • The de Broglie hypothesis, formulated in 1924, predicts that particles should also behave as waves.
  • The wavelength of an electron is given by the de Broglie equation $\lambda = \frac{h}{p}$.
  • $\lambda$ is called the de Broglie wavelength.
  • In these instruments, electrons are accelerated by an electrostatic potential in order to gain the desired energy and, thus, wavelength before they interact with the sample to be studied.

• Electron Microscopes

  • This is because their de Broglie wavelengths are so much smaller than that of visible light.
  • You hopefully remember that light is diffracted by objects which are separated by a distance of about the same size as the wavelength of the light.

• de Broglie and the Bohr Model

  • By assuming that the electron is described by a wave and a whole number of wavelengths must fit, we derive Bohr's quantization assumption.
  • Bohr's condition, that the angular momentum is an integer multiple of $\hbar$, was later reinterpreted in 1924 by de Broglie as a standing wave condition.
  • Substituting de Broglie's wavelength of $\frac{h}{p}$ reproduces Bohr's rule.
  • Schrödinger employed de Broglie's matter waves, but instead sought wave solutions of a three-dimensional wave equation.
  • (a) Waves on a string have a wavelength related to the length of the string, allowing them to interfere constructively.

• Particle-Wave Duality

  • De Broglie's wave (matter wave): In 1924, Louis-Victor de Broglie formulated the de Broglie hypothesis, claiming that all matter, not just light, has a wave-like nature.
  • The wavelength of the matter wave associated with a baseball, say moving at 95 miles per hour, is extremely small compared to the size of the ball so that wave-like behavior is never noticeable.

• The Photoelectric Effect

  • This question would be resolved by de Broglie: light, and all matter, have both wave-like and particle-like properties.

• The Physics of Bremsstrahlung

  • Typically over distances less that the de Broglie length of the electron one must treat the problem quantum mechanically,

• Quantum Numbers

  • While the work of Bohr and de Broglie clearly established that electrons take on different discrete energy levels that are related to the atomic radius, their model was a relatively simplistic spherical view.

• The Uncertainty Principle

  • Roughly, the uncertainty in the position of a particle is approximately equal to its wavelength (λ).
  • The uncertainty in the momentum of the object follows from de Broglie's equation as h/λ.