Chapter 41 wave mechanics national tsing hua university. It basically describes the wave nature of the electron. The wavelength of the wave depends on the mass and the velocity of the particle. Using this equation the energy may be rewritten as. What is the magnitude of the velocity of this electron. For example, calculate the wavelength of a wave associated with a 1. The total energy of moving particle is given by e k. Enter the weird and wonderful world of wave particle duality. Solution when a charge is accelerated from rest through a potential difference v, its gain in kinetic energy, mv2, must equal the loss in potential energy qv. An alternate and also correct version of this formula is.
He proposed that all particles have a wavelength given by. But then, the wave nature of electromagnetic radiation is called into question when it is involved in blackbody radiation, photoelectric e ect and such. Where is the mass of the particle and is the speed of light. He received the 1929 nobel prize in physics for this work. Astronomers estimate that our galaxy has a mass of 4. But then, the wave nature of electromagnetic radiation is called into question when it is involved in blackbody radiation, photoelectric e. By rearranging the momentum equation stated in the above section, we find a relationship between the wavelength. Electromagnetic radiation, exhibit dual nature of a particle having a momentum and wave expressed in frequency, wavelength. Its not that this work was the most significant, but, this wavelength. Matter wave simple english wikipedia, the free encyclopedia. This equation simply relates the wave character and the particle character of an object. Matter waves istituto nazionale di fisica nucleare.
The dispersion relation of d e broglie waves includes the rest mass, but the schrodinger equation does not. Note that this is the same equation that applies to photons. Electron microscope is a common instrument illustrating this fact. Basing his formula on earlier formulas, he arrived at the equation below. Thisequation suggeststhat every particle has a wavenature, with a wavelengthgivenby the. Thus, every object in motion has a wavelike character.
Nov 21, 2016 enter the weird and wonderful world of wave particle duality. There must be a correct way of deriving it for electrons etc. This worksheet comes complete with a full answer sheet and extension questions to keep those advanced boffins busy. It is represented by the wavelength of a wave traveling at constant speed is given by. The debroglie wavelength will be our primary physics input for the development of quantum mechanics.
But in the end one cannot derive this relationship. The quantum number n of an orbit is the number of electron waves that fit into the orbit. There is no chance of observing wave phenomena, such as diffraction, with macroscopic objects. Quantum physics i, lecture note 4 mit opencourseware.
By analogy with the wave and particle behaviour of light that had already been established experimentally, the french. An electron and a photon each have a wavelength of 2. Find the wavelength of an electron moving with a speed of ms1. The same formula gives the momentum of an individual photon associated with a light wave of wavelength. Photons dont have mass, but you can use the equation to find the momentum of a photon. In relating a particles energy to its wavelength, two equations are used. Bohrs model of the atom was valuable in demonstrating how electrons were capable of absorbing and releasing energy and how atomic emission spectra were created.