![]() ![]() In 1937, the Nobel Prize in Physics was awarded to Clint Davisson and George Thomson (son of J.J. In 1927, experiments were done that showed electrons behaved as a wave (by showing the property of diffraction and interference patterns). In 1926, de Broglie predicted that matter had wave-like properties. ![]() You can't do that with the short wavelengths of heavier particles (see examples below). This turned out to be very important because one could then take a beam of electrons and perform experiments with detectable results. Our electron's wavelength is almost 3000 times shorter than our ultraviolet example and its wavelength puts it in the X-ray region of the electromagnetic spectrum. I'd like to compare this wavelength to ultraviolet light, if I may. All three of them are under the radical sign. Just to be sure about two things: (1) the unit on Planck's Constant is Joule-seconds, both are in the numerator and (2) there are three values following the radical in the denominator. When I use this value just below, I will use J (for Joules).Ģ) Next, we will use the de Broglie equation to calculate the wavelength: X = 1.28433 x 10¯ 17 kg m 2 s¯ 2 (I kept some guard digits) Problem #1: What is the wavelength of an electron (mass = 9.11 x 10¯ 31 kg) traveling at 5.31 x 10 6 m/s?ġ) The first step in the solution is to calculate the kinetic energy of the electron: To those of you reading this, best wishes with your continued studies! The classical momentum of the particle is the group velocity of a wave packet, which turns out to be p/m, but the analysis takes about one week of a QM class.Īt this point, we are beyond what the ChemTeam understands. No, the v that you are calculating is not the classical momentum of the particle: it is the phase velocity of the wave. Now comes the question: Should not the velocity of an electron be v = p/m? (ChemTeam comment: replace p with mv to get mv/m = v.) The posted answer was this: Look at (1/2) p 2/m and substitute mv for the p: (ChemTeam comment: note the use of the two de Broglie equations.)ĬhemTeam comment (including the indented equations just below): remember that p is momentum and that p = mv. Suppose an electron has momentum equal to p, then its wavelength is λ = h/p and its frequency is f = E/h. The second de Broglie equation is this: ν = E/hĪ) ν stands for frequency (sometimes ν is replaced by f) it is here in case you migt be interested in it. I do not use it in any of the examples problems to follow. You may skip the following discussion of the second de Broglie equation. We will use this result in the example problems that follow. ![]() ![]() We can now substitute that into the de Broglie equation: Just above, we developed that p = √(2Em). (I will discuss the second de Broglie equation below the following example problems.)Ī) λ stands for the wavelength of the particleĬ) p stands for the momentum of the particle He received the 1929 Nobel Prize in Physics for this work. You can read more about de Broglie's work here. It is one of two related equations called the de Broglie equations. Here's a key point from physics: mv is a particle's momentum. You really do need to keep the difference between a symbol and a unit clear in your mind. Here's one last confusing thing to make you feel better: the name (as opposed to the symbol) of the KE unit is Joule. That means the unit (m/s) gets both the length (unit = m, meaning meters) and the time (unit = s, meaning seconds) get squared. Remember that the velocity (symbol = v) is squared. One possible point of confusion: The unit m means meters, the symbol m means mass. The unit on velocity is meters per second, most usually written m s¯ 1 (it can also be written m/s). That means, if you get a mass in grams given in the problem, you must convert it to kilograms. Next, some comments on the units attached to the numerical values represented by the symbols in the kinetic energy equation. For example, the symbol P stands for the pressure and the unit on the numerical value for pressure is atm. I would also like to emphasize that these symbols are not the units. Another example of an equation using symbols is PV = nRT. I would like to emphasize that these are symbols, which are standing in place of the actual numerical values. There are three symbols in this equation: (The second equation is down the page a bit.) The first is the kinetic energy equation: In relating a particle's energy to its wavelength, two equations are used. The deBroglie Equation: Relating a Particle's Energy to its Wavelength The deBroglie Equation: Relating a Particle's Energy to its Wavelength ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |