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Repeat the previous problem for a 10.0-nm-wavelength photon.

a) $6.63\times 10^{-26} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$b) $7.28 \times 10^{4} \mathrm{m} / \mathrm{s}$c) $8.25 \times 10^{3}$

Physics 103

Chapter 29

Introduction to Quantum Physics

Quantum Physics

Hope College

University of Sheffield

McMaster University

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in this problem, we're asked to calculate the moment. Um, of a photon for part came So this moment, um of a photon can be found by doings, Planks constant divided by wavelength And our wavelength given in the problem is 10 times 10 centimeters. So this is 6.63 times 10 to the negative 34 jewels. Time seconds divided by our given wavelength of 10 times 10 to the negative night meters. So that's nano meters corrected two meters. And this gives us a moment, um, of 6.63 times 10 to the negative 26 kilograms meters per second and for part B were asked to calculate what the velocity of an electron would have given the same momentum. So mo mentum is mass times velocity. So velocity is mo mentum divided by mass. So 6.63 times 10 to the negative 26 divided by the mass of an electron which is 9.11 times 10 to the negative 31 kilogram pes to give us a velocity of 7.28 times 10 to the fourth meters per second. And then we're asked to compare the energy of a electron compared to the energy of a proton. So to find the energy of our electron, we can do 1/2 m V squared. So 1/2 9.11 times 10 to the negative, 31 times the velocity that we just found 7.28 times 10 to the fourth squared to give us an energy of 2.41 times 10 to the negative 21 Jules and then our energy of our approach I'm sorry of our photon will be determined using our momentum of our photo on times the speed of light. So we found our momentum to be 6.63 times 10 to the negative 26 and then our speed of light is 2.99 times 10 to the eighth meters per second, giving us an energy of 1.99 times 10 to the negative 17. And if we divide our energy of our photon divided by the kinetic energy of our electron, we get a value of eight point to five times 10 to the third, which tells us that our energy of our photon is 8.25 times 10 to the third times greater than the energy of our electron

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