Get this resource as part of a bundle and save up to 33%. Similarly to right the wavelength of the xray, we can use planks quantum concept as shown below. A person entering a room with more than one entrance will always enter through one of them, not all of them at the same time. The problem as i see it with defining the relativistic wave momentum as.
It can also be applied to other particles such as electrons and protons. Solved problems on quantum mechanics in one dimension. A majority of waveparticle duality problems are simple plug and. We point out as the just given demonstration, with postulate 2. Plancks investigation of the emission spectra of hot objects and the subsequent studies into the photoelectric effect had proven that light was capable of behaving both as a wave and as a particle. So, we will look at just a lone bohrs model of the hydrogen atom in an empty void of space.
What is the debroglie wavelength of an electron with 10 mev of kinetic energy. An electron of charge e and mass m is accelerated from rest by a potential difference v. It contains plenty of examples and practice problems. Additionalandadvancedproblems university of minnesota duluth. Compare with compton wavelength of the particle formally speaking, c. No ad hoc solutions are proposed for individual problems. The two methods and their combination have enabled theoreticians to address problems heretofore unsurmountable and have reported much success. Determine the kinetic energy in electron volts required for electrons to resolve a large organic molecule. It seemed reasonable to wonder if electrons could also have a dual waveparticle nature. Strategy we combine the first quantization condition in equation \ref6.
Thus, every object in motion has a wavelike character. Schrodinger believed that a particle is really a group of waves, a wave packet. Electron microscope is a common instrument illustrating this fact. According to einsteins theory of special relativity, the mass of a particle is affected by its velocity. This brought together the relationship of the mass of a photon and speed of light with the photon energy. My goal was to simplify the situation as much as possible. Solution equate the wavelength of an electron and the wavelength of an x. Equate the wavelength of an electron and the wavelength of. Scintillators are materials that produce light when they are exposed to radiation. He used a combination of quantum theory and special relativity to propose that the wavelength. What would the wavelength of the helium atom be if it were traveling at the same speed as the electron in part a 1 amu 1. M k b t, which provides another characteristic length for this uniform ideal gas.
This formula relates the wavelength to the momentum of a wave or particle. The problems are from chapter 5 quantum mechanics in one dimension of the course text modern physics by raymond a. When the problem involves a nonrelativistic object moving with a nonrelativistic speed u, such as in. Emc 2 mmass of photon cspeed of light combined with plancks equation.
Comptons formula established that an electromagnetic wave can behave like a particle of light when interacting with matter. Extra challenge problems debroglie wavelength 1 debroglie. The speed of the matter wave is the speed of the particle. What is the debroglie wavelength of an electron with. Solved problems on matter waves ubc physics university of. By rearranging the momentum equation stated in the above section, we find a relationship between the wavelength. What is the debroglie wavelength for each of the following particles. For an object to have a wavelength, it must be moving. The same formula gives the momentum of an individual photon associated with a light wave of wavelength. Solution equate the wavelength of an electron and the wavelength of an. In the intrinsic system of the corpuscle in the sense of the relativity theory. Problem \\pageindex1\ assume the mass of an electron is 9. Oct 17, 2008 homework statement a 220lb fullback runs the 40yd dash at a speed of 19.
What i confuse is if the momentum in relativistic limit change to texp \gamma mv tex, so do we need to apply the length. But then, the wave nature of electromagnetic radiation is called into question when it is involved in blackbody radiation, photoelectric e. A small object can be observed by a wave if the wave can be e ectively scattered by the object. Electrons diffracted after being reflected off a single crystal of nickel. Scribd is the worlds largest social reading and publishing site. Understand the relationship between the schrodinger equation and quantum mechanics. Thermal wavelength an overview sciencedirect topics.
Equate the wavelength of an electron and the wavelength of an. Quantum physics i, lecture note 4 mit opencourseware. When solving numerical problems in quantum mechanics it is useful to note that the product of. In particular, one has not been able to achieve the ultimate goal, namely a undulatory theory of matter within the framework of. To produce the same diffraction pattern, the electrons must have the same wavelength as the xrays. The observed electron intensity distribution is plotted in the figure. Schrodings success in tackling several problems confirmed that the wave mechanics was an important advance. So recapping, light can have particlelike or wavelike properties, depending on the experiment, and so. We are given the wavelength of an electromagnetic wave and asked to calculate the frequency. Chem 101 answer to homework problems 4th edition chapter 6. Scintillators are materials that produce light when they are exposed to. Here in the place of the momentum we can write applied potential and the corresponding energy.
Determine the electron energy ev, momentum, and velocity. This happens if the objects size and the wavelength of the wave are about the same. Articulate the implications of the heisenberg uncertainty principle. If e is the kinetic energy of the material particle of mass m moving with velocity v,then. Calculate the wavelength of an electron traveling with a speed of 2.
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