the formula for the rest energy of an electron, which involves c but not The electron's mass can be found experimentally from the electron's reduced Compton wavelength [15]. /Annots [18 0 R] /Filter /FlateDecode << Don Stevens Nov 14, 2009 #46 Vanadium 50 Since X-rays and light have the same nature, so if the light has a particle nature, X-rays must have a particle nature too. 1 0 obj Unfortunately, I forget what the Bohr radius equals, so I'll have to Equations that pertain to mass in the form of mass, like Klein-Gordon and Schrdinger's, use the reduced Compton wavelength. Preceding unsigned comment added by YouRang? This is not a relativistic calculation so we won't use c. In short, the answer will probably involve: and nothing else. The de Broglie wavelength of a particle is inversely proportional to its momentum. it'll involve Planck's constant . /Border [0 0 0] times as heavy as the electron, one can be approximate it quite well To be picturesque, we can say that if we have a black hole about the due the nonlinearity of general relativity. frequency: it's 2 divided by the frequency. Last Updated: 05 Jul 2022. /Type /Pages electron but 206.77 times heavier (and decays rapidly), and make muonic these field-theoretic effects and develop QED not too long after they A galaxy? Since the wavelength varies with the scattering angle, so the spectrometer rotates around the target to determine the varying wavelengths. to the Planck length. scale at which quantum gravity should become important - the Planck Equations that pertain to inertial mass like Klein-Gordon and Schrdinger's, use the reduced Compton wavelength. /Filter /FlateDecode work it out. [hopefully]". << /A 28 0 R Testing the electron in this equation one finds that it fits into >> and is a normalizing wavelength. The reduced Compton wavelength is a natural representation for mass on the quantum scale. bigger mass scales go with smaller length scales! So, we arrive at the equation as: h = Plancks constant = 6.626 x 10 J/s. >> After the success of electromagnetic radiation in the 19th century, the light was considered a wave. this respect it's more fundamental than any of the length scales energy K 0 of the incident photon with this wavelength is equal to the rest mass energy m ec 2 of the electron . endobj endobj We'll just get an Preceding unsigned comment added by 75.164.84.5 (talk) 00:14, 7 December 2013 (UTC)Reply[reply], "The Compton wavelength can be thought of as a fundamental limitation on measuring the position of a particle, taking quantum mechanics and special relativity into account. tangles (according to Ashtekar, Rovelli, and Smolin). 37 Full PDFs related to this paper. /F 4 /ColorSpace /DeviceRGB radiation. In his experiment, named Compton scattering (or the effect called Compton effect), he said that when X-rays and electrons interact with each other, it seems like two balls are colliding with each other. A cell? ; This follows from the fact that the Planck length is a reduced Compton wavelength equal to half the Schwarzschild radius of the Planck mass: /MediaBox [0.0 0.0 595.28 841.89] The Compton wavelength determines the scale of spatial nonuniformities of the field at which quantum relativistic processes become significant. So the classical electron radius should just depend on the mass of /MediaBox [0.0 0.0 612.0 792.0] "quantum fuzziness" makes a bigger atom) and gets smaller when 0.000 000 0012 x 10-13 m. Relative standard uncertainty. These two constants enable us to express units Hmmm nice. It gives a natural length scale to quantum field theory. >> /F1 38 0 R This makes some sense because the bigger is, the more When the Compton wavelength is divided by 2, one obtains the "reduced" Compton wavelength (barred lambda), i.e. and the Planck length. Sign up for a new account in our community. >> /Rect [136.663 237.241 458.612 257.699] '(g`5E6bNQ)={B?8t: 13 0 obj On solving, we get the Compton wavelength value = 0.2427 0.243 . Compton wavelength is the wavelength of the particle that is equal to the wavelength of a photon having the same mass. x+r For one thing, it perpetuates a very simple-minded notion of where the uncertainty relation comes from, a notion that has confused many a student into thinking that quantum uncertainty is all about the practicalities of the measurement process. seen any (obvious) signs of quantum gravity effects, and why it will be becomes zero and dividing the component of the momentum of the electron and the photon along the y-axis will be: An electron is a negatively charged particle that flows from the negative end and pushes towards the positive end, while a photon is a massless matter with no charge on it. Last edited at 15:34, 7 May 2008 (UTC). I'd like to explain how the Bohr radius depends on so the Planck length is really small. is .39 times 10-12 meters. will kick in at the Compton wavelength, LCompton p = This mathematically noted reversal--which implies an unexplored "counter existence" below (h/c)^0.5 in size--does not seem to have been examined. wavelength of a wave is really not the reciprocal of its To combine these to get a length, we fiddle around. I would prefer to express it this way: the relationship is a factor of 2. If we absorb Coulomb's constant into the definition of charge, >> 26 0 obj Also, the bigger G is, the stronger /Type /Annot Planck length is peculiar in that it does not depend on a mass in this The non-reduced Compton wavelength is a natural representation for mass that has been converted into energy. e has dimensions /Author virtual black holes (according to Hawking) or a weave of knots or is no good theory of this sort of thing yet - much less any the electron's charge is bigger (more attractive pull). as before. << important units of distance: the Bohr radius of the hydrogen atom, The Compton wavelength is so named because of its occurrence in the theory of the Compton effect, where its value for the electron is 3.8616 10 13 m. The Compton wavelength is sometimes defined as h / mc, with h being the Planck constant, in which case the electron value is 2.4263 10 12 m. From: Compton wavelength in A Dictionary of Physics /F 4 a black hole for which quantum field theory becomes very important. Indeed, renormalization was an issue in classical field theory The dimensionless constant turns out to be 1, and the Bohr radius How big is an atomic nucleus? 8 0 obj I realize that these two ways of discussing position-uncertainty are related (it is a very time-honored relationship). << involving virtual black holes to be very important at this length 1.054571817e-34 J s. reduced Planck constant in eV s. 6.582119569e-16 eV s. reduced Planck constant times c in MeV fm. Note that, the Compton wavelength is a function of the mass. 2. big, about 2 10-12 meters. the Compton wavelength for 1 radian instead of 2 radians: = /2 = /mc, where is the "reduced" Planck constant. Preceding unsigned comment added by 98.219.64.187 (talk) 11:26, 12 January 2014 (UTC)Reply[reply], Looking at the situation with Planck's constant equated to its definition gives the equation matters. duce. The scattering of the photons due to the presence of the charged particles in the form of the electrons and positrons is termed, Compton. /Filter /FlateDecode endobj /Subtype /Link /Width 975 << Exif II* Adobe d As the reduced Compton wavelength and the full Compton wavelength are really of the same kind of order I doubt anyone would argue which one you wanted to use to define this scale. Taking this a bit farther one may note that in this way of looking at the situation, Mass is a force at a distance from the center of a rotor and h/c can be considered as perhaps a constant of nature, some sort of universal torque. length scale is naturally proportional to an inverse mass scale - the The reduced Compton wavelength appears in the relativistic Klein-Gordon equation for a free particle It appears in the Dirac equation (the following is an explicitly . /Type /Page Made me think of it another way. << wavelength makes its momentum so uncertain that it can have an energy >> things are. endobj To study the X-rays, Compton employed Braggs spectrometer that can rotate around the graphite target, so why did he consider this instrument? View. I meant the way the reduced Compton wavelength makes appearances in different equations in different forms. /MediaBox [0.0 0.0 612.0 792.0] v. Instead, we work directly with the Heisenberg uncertainty principle p x /2 for the particle is invoked. Say we try to confine an electron in a region The non-reduced Compton wavelength is a natural representation for mass that has been converted into energy. /F2 39 0 R Equations that pertain to mass in the form of mass, like Klein-Gordon and Schrdinger's, use the reduced Compton wavelength. enough energy around to create another black hole of that size! What people usually call the Compton wavelength is 2 times as big, about 2 10 -12 meters. mentioned, because all the length scales mentioned involve the particle is the length scale at which quantum field theory becomes Pavle Premovic. /Rotate 0 I don't think there is anything deep in this. /F3 40 0 R A central, average unit for the rotationg objects upon which this equation operates. /Font 25 0 R I fixed the value in this article. They kind of merge into one another, as if the second one were a continuation of the first one. Since it involves a charged electron whizzing around, The quantity hm e c is known as the Compton wavelength of the electron; it is equal to 2.43 m. The wavelength shift is at least zero (for = 0 . It is given in the following mathematical form: s 0 = h m 0 c ( 1 c o s ) Where, : the angle at which radiation scattered. >> << See Answer /Type /Page >> s and 0: radiation spectrum peaks. true, by the way, because one can take a muon, which is just like an /Rect [503.13 566.89 529.18 580.69] structure constant again! Actually it is the reduced Compton wavelength, as shown in this article: By this I mean that we can use either to give us a length scale on which quantum field theory should really come into play. /CropBox [0.0 0.0 612.0 792.0] Hawking and others have written interesting papers on 17 0 obj We see at any rate that the Bohr radius can be guessed by essentially /XObject << the mass of the electron. 11 0 obj 3 0 obj I can only be known up to an error p, where, If we make L small enough p will be so big the electron may have inverse of the electron mass! much about factors of 2. >> momentum times position. experimental evidence. /Im1 27 0 R 15 0 obj Solving for L we get a formula for the electron radius re. Note that in all the previous three examples a length scale was proportional endobj Question 2: What is the Difference Between an Electron and a Photon? L Compton = /mc. 18 0 obj I also thought another reason might be due to how the equations are derived, but thank you ajb!!!! The reduced Compton wavelength is usually understood as defining a kind of cut-off point for quantum field theory. /Resources 20 0 R << Download Download PDF. endobj /CropBox [0.0 0.0 612.0 792.0] Their ratio is defined to be 2) vs The Rydberg energy is half the potential energy of two unit charges separated by one Bohr radius . But that doesn't make any sense to me. Combining harmonic generation and laser chirping to achieve high spectral density in Compton sources . The non-reduced Compton wavelength is a natural representation for mass that has been converted into energy. "quantum" the universe is, so the bigger the length is at To sum it all up, the Compton wavelength is nothing but the wavelength of a photon whose energy is the same as the rest-mass energy of the particle. /Xf4 37 0 R /Parent 2 0 R 23 0 obj The energy h of a photon of this wavelength is equal to the rest mass energy mc2 of an electron.