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 Advanced Mechanics Advanced Mechanics Physics Help Forum Jun 12th 2011, 12:29 AM #1 Junior Member   Join Date: Jun 2011 Posts: 3 Find Electron Velocity How does the velocity of a falling electron change as it falls toward a proton? As the distance between a stationary proton and a moving electron toward the proton decreases by factors of 10, what factor is the increase in velocity? Assume the distance between the proton and electron starts at 1,000 meters, then what is the velocity of the electron at 1,000 meters, 100 meters, 10 meters, 1 m, O.1 m, 0.01 m etc. I'm wondering as the distance decreases by a factor of 10, does the velocity increase by a factor of a 100 or what? That is my interest in the solution! My attempt at a solution is as follows: a0 = F / m = 253.27 / x0^2 [m / s^2] a1 = 253.27 / x1^2 a01 = (a0 + a1) / 2 (x0 - x1) = 0.00001 = x01 (t1 - t0) = ((x0 - x1) / a01))^0.5 v0? = (x0 - x1) / (t1 - t0) v1? = ((v0^2 + 2 * a01 * (x0 - x1))^0.5 The above requires a computer solution as (x0 - x1) = 0.00001 changes by amounts of 0.00001 to (x1 - x2) = 0.00001, etc. I have no requirement to write any software or to solve this problem. Perhaps such software exists? My interest is theoretical in what the electrical field around the proton is? Could this electric field be made of ultra small particles of mass coming off the proton? This positron mass would decrease by a factor of 100 as the radius increases by a factor of 10. What is your opinion and hopefully an answer to my velocity interest? __________________________________________________ ___________________________________________ I solved the problem using coulombs energy equation replacing charge q with the number of charged particles n as follows: Fr = 2.3071 E-28 (n1) (n2) / r = m (v ^2) / 2 2.3071 E-28 / 9.1094 E-31 = 253.27 v = (506.54 / r) ^0.5 r0 = 1 E+0 m then v = 22.506 m / s r1 = 1 E-1 m then v = 71.172 m / s r9 = 1 E-9 m then v = 7.1172 E+5 m / s r10 = 1 E-10 m then v = 2.2506 E+6 m / s The factor velocity increase when r decreases by a factor of 10 is: r1 / r0 = 71.172 / 22.506 = 3.1622 r10 / r9 = 2.2506 E+6 / 7.1172 E+5 = 3.1622 The factor velocity decrease when r increases by a factor of 10 is: r0 / r1 = 22.506 / 71.172 = 0.31622 r9 / r10 = 7.1172 E+5 / 2.2506 E+6 = 0.31622 Solved! __________________________________________________ ___________________________________ The general solution to find the velocity of the falling electron to a nucleus with n protons is as follows: v = 22.506 (n / r) ^0.5 v1 = v2 (r2 / r1) ^0.5 v2 = v1 (r1 / r2) ^0.5 Last edited by DKseed; Jun 13th 2011 at 09:40 PM. Reason: Below I solved for the general solution of a falling electron to a nucleus with n protons   Jun 13th 2011, 12:59 AM #2 Physics Team   Join Date: Jun 2010 Location: Mauritius Posts: 609 I'm not sure where you're getting your values... anyway, this is how I would have done it: I will first assume that the velocity of the electron is 0 when it is 1000 m away since yo said it 'starts' there. I will not go around using the basic equations of motion since the acceleration is not constant. The force acting on the electron varies as the distance varies and this will be a real pain to find the acceleration at each and every point in between the points you want to get the velocity. Instead, it's easier to go around energy equations. Potential energy 1000 m away from the proton: Using the values that we have: Now, at 100 m; And so on. The velocity at 100 m is given by the kinetic energy formula and the change in potential energy. Lost in PE = Gain in KE You solve for v. To get the velocity at 10 m, you use: http://latex.codecogs.com/gif.latex?...\frac12%20mv^2 (the site wouldn't let me post a 5th image... -.-" ) And so on. I hope it helped! PS: Eo [ Epsilon nought is the permittivity of free space and is a very small value. There are some schools which teack V = kq/r though, where k = 1/(4pi Eo) ] __________________ Jerry (Got my results!) It is easier to protect your feet with slippers than to cover the earth with carpet. No one can go back and change a bad beginning; but anyone can start now and create a successful ending. If a problem can be solved, no need to worry about it. If it cannot be solved what is the use of worrying?  Tags electron, electron velocity, falling electron, find, velocity Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Physics Forum Discussions Thread Thread Starter Forum Replies Last Post bes Advanced Electricity and Magnetism 1 Jun 28th 2015 11:43 AM s3a Electricity and Magnetism 1 Jan 27th 2011 08:22 PM jawad khan Advanced Electricity and Magnetism 1 Dec 3rd 2009 03:54 AM Dumkoff Electricity and Magnetism 0 Apr 7th 2009 09:05 AM Aryth Special and General Relativity 6 Apr 17th 2008 05:03 AM