Another Felix Posted May 16, 2015 Share Posted May 16, 2015 Please, I need to go over some questions from my previous exams in the class, but my teacher apparently doesn't respond to emails or have office hours, so here I am to ask random strangers on the internet. Just going to post the questions here, and any and all help is greatly appreciated. May Arceus bless all of you. The kinetic energy of the body equals its rest energy. What is the speed of the relativistic body? Radiation of wavelength 124 nm (nano-meters) falls on a material with work function 4.5 eV (electron volts) a) What is the maximum value of kinetic energy EK that the emitted electrons have (in eV)? What is the value of kinetic energy Ek, if the value of the wavelength is 300 nm? Explain. Prove that the fine structure constant appha (he probably meant to write alpha) = v1 / c (c = speed of light = 3*108 m/s) where v1 is the nonrelativistic speed of an electron on the first Bohr orbit, equals 1/137 X=ray photons are scattered off by a small cloud of free stationary electrons. Photons are observed to have scattered exactly backwards. In this case, what is the relative value (in percent) of the wavelength shift of the incident photons if the initial wavelength is .04 nm? Calculate the wavelength of a photon required to raise an electron from the second excited state to the third excited state of hydrogen. How many times the radius of the electron orbit in the first excited state is bigger than the radius of the ground state in the Bohr model of Hydrogen? Find the wavelength of a relativistic electron with kinetic energy Ek = 1.51 MeV (Mega electron Volts) and also the wavelength of a neutron with the same energy. Again, any help you can provide is greatly appreciated. Quote Link to comment Share on other sites More sharing options...
NickCrash Posted May 16, 2015 Share Posted May 16, 2015 Haven't done physics in years, but I'll give it a go, since nobody has commented so far. I'll answer mainly with theory, so you'll actually do the calcs. Sorry but it's too late for me to actually sit down and do them myself. About the first, it seems to be one direction mechanics where E=K+U, where K=1/2 m u^2 and U=mgh When at rest K=0, so E=mgh, therefore 1/2mU^2=mgh =>U^2=2gh Unless you need something else, just apply the root. About the second, in order for max kinetic E, the electron should be in the outer orbit. That's already given in 4.5eV. Now the energy of a photon is E=hv, where h=planck constant and c=v*λ, where λ=wavelength and v=frequency. Apply and solve. E=hc/λ. Find the energy and reduce 4.5eV from that Got tired. Good night edit: btw the 2nd excited orbit is the 3rd orbit. Quote Link to comment Share on other sites More sharing options...
Another Felix Posted May 16, 2015 Author Share Posted May 16, 2015 Sorry Wade, but the first question solution you attempted is wrong. It's relativity, not standard mechanics. Since it's asking for KE, there needs to be some kind of V. KE = Erest Erest = mc^2 KE = (gamma -1) mc^2 gamma = 1/(1-v^2/c^2)1/2 mc^2 = ((1/(1-v2/c2)1/2 - 1) * mc^2 And then I just need to solve for v. Think I've got this one. Second one you tried posting an answer to... yeah, that checks out. Egamma = Fi + KE, so KE = Egamma - Fi Fi = Wave function = 4.5 eV Egamma = hc/lambda = 1240eV/124nm = 10 eV * nm KE = 10 eV * nm - 4.5 eV = 5.5 eV * nm. Many thanks though, King Deadpool. Quote Link to comment Share on other sites More sharing options...
Another Felix Posted May 18, 2015 Author Share Posted May 18, 2015 I've got one more question, this time math. I know I'm not supposed to double post, but I need help here and would have to bump the board to do so. Find all second order partial derivatives of the function: f (x,y) =x2 * ey This one is probably easier than the others, but I still need help. Quote Link to comment Share on other sites More sharing options...
Void Posted May 19, 2015 Share Posted May 19, 2015 yeah this should be pretty simple, just differentiate twice while treating y as a constant, then differentiate twice treating x as a constant you should get: fxx = 2ey fyy = x2ey Quote Link to comment Share on other sites More sharing options...
Kookies Posted May 19, 2015 Share Posted May 19, 2015 (edited) 1st problem (KE+mc2)2=c2p2+m2c4 so you can solve for p=3(1/2)mc= mvgamma so solve for v which is v=3(1/2)c/2 2nd problem E(eV)=1.24/wavelength(micrometers)=10 eV so max KE=E-W=5.5eV you do the same for the second part of the question 3rd problem Centripital Force=mv2/R= kq^2/R^2= Coulomb you find R from bohrs theory and then solve for v and thenyou can find alpha 4th problem Δλ=λc(1-cosθ)=2λc=2h/(mc) so you want Δλ/λinitial*100% 5th problem ΔΕ=Ε1/4-Ε1/9=hc/λ solve for the wavelength when E1=13.4eV rn=n*r1 for the nth excited state 6th problem is the same with the first find the momentum and then you can find waveength by the De Broglie formula... yeah this should be pretty simple, just differentiate twice while treating y as a constant, then differentiate twice treating x as a constant you should get: fxx = 2ey fyy = x2ey you also have fxy=fyx=2xey Had fun with these simple exercises... Edited May 19, 2015 by Kookies Quote Link to comment Share on other sites More sharing options...
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