Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 39, Problem 50P
To determine
To prove that free electron cannot absorb or emit a photon.
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Chapter 39 Solutions
Physics for Scientists and Engineers
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- Consider A Relativistic Particle,whose de-Broglie wavelength Is λR . If λc represents Compton wavelength, Then Find The Ratio λR/λc ?arrow_forward(a) A particle with mass m has kinetic energy equal to three times its rest energy. What is the de Broglie wavelength of this particle? (Hint: You must use the relativistic expressions for momen- tum and kinetic energy: E2 = (pc2) + (mc2)2 and K = E - mc2.) (b) Determine the numerical value of the kinetic energy (in MeV) and the wavelength (in meters) if the particle in part (a) is (i) an electron and (ii) a proton.arrow_forwardThis question is for modern physics and wave and particle: (a) To how small a region must an electron be confined for borderline relativistic speeds – say, 0.05c – to become reasonably likely? (Ans: 3.9×10^−12m ) (b) On the basis of this, would you expect relativistic effects to be prominent for hydrogen’s electron, which has an orbit radius near 10-10? For a lead atom “inner-shell” electron of orbit radius 10-12m?arrow_forward
- In quantum interpretation of the electromagnetic waves in vacuum the photon has the energy E = hw/2n and the momentump= hk/2n. So the ratio E of the energy to the momentum is = c, the speed of light in k vacuum. Similar relation can be obtained in classical electrodynamics as follows. Consider the time-averaged energy density of the electromagnetic field ɛ = B² /2µ0 + €0 E² /2 for a plane wave propagating in vacuum along the z-direction. Calculate the time-averaged energy flux (Poynting flux) for such a wave S = E × H and confirm that its ratio to the time-averaged energy density ratio is equal to the speed of light in vacuum, S/e = c.arrow_forward(a) Calculate the de Broglie wavelength of a proton (rest mass 938.3 MeV/c2) with kinetic energy 10 MeV. (b) Calculate the de Broglie wavelength of an electron (rest mass 0.51 MeV/c2) with energy 10 GeV.arrow_forwardFor a free relativistic quantum particle moving with speed u, the total energy of the particle is E = hf = hω = √p2c2 + m2c4 and the momentum is p = h/λ = hk = γmu. For the quantum wave representing the particle, the group speed is υg = dω/dk. Prove that the group speed of the wave is the same as the speed of the particle.arrow_forward
- An antiproton has the same mass and rest energy (938.3 MeV) as a proton, but has a negative change -e instead of the positive charge +e of the proton. A proton and an antiproton, initially far apart, move toward each other with the same speed and collide head-on, annihilating each other and producing two photons. Find the energies and wavelengths of the photons if the initial kinetic energies of the proton and antiproton are (a) both negligible and (b) both 545 MeV.arrow_forwardA neutron of mass 1.675 × 10-27 kg has a de Broglie wavelength of 7.8x10-12 m. What is the kinetic energy (in eV) of this non-relativistic neutron? Please give your answer with two decimal places. 1 eV = 1.60 × 10-19 J, h = 6.626 × 10-34 J ∙ s.arrow_forwardA quantum particle of mass m is placed in a one-dimensional box of length L. Assume the box is so small that the particle’s motion is relativistic and K = p2/2m is not valid. (a) Derive an expression for the kinetic energy levels of theparticle. (b) Assume the particle is an electron in a box of length L = 1.00 × 10-12 m. Find its lowest possible kinetic energy. (c) By what percent is the nonrelativistic equation in error?arrow_forward
- Assume that the total energy E of an electron greatly exceeds its rest energy E0. If a photon has a wavelength equal to the de Broglie wavelength of the electron, what is the photon’s energy? Repeat the problem assuming E= 2E0 for the electron.arrow_forwardDetermine the de Broglie wavelength of a particle of mass m and kinetic energy K. Do this for both (a) a relativistic and (b) a nonrelativistic particle.arrow_forwardHelp Mearrow_forward
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