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Construct Your Own ProblemConsider a highly relativistic particle. Discuss what is meant by the term "highly relativistic." (Note that, in part, it means that the particle cannot be massless.) Construct a problem in which you calculate the wavelength of such a particle and show that it is very nearly the same as the wavelength of a massless particle, such as a photon, with the same energy. Among the things to be considered are the rest energy of the particle (it should be a known particle) and its total energy, which should be large compared to its rest energy.

$\lambda_{\text {photon }}=\lambda_{\text {electron }}=1.08 \times 10^{-13} \mathrm{m}$

Physics 103

Chapter 28

Special Relativity

Relativity

Rutgers, The State University of New Jersey

Simon Fraser University

McMaster University

Lectures

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but they're letting mystic Total energy is given by e is equal to Goma times M c square where go my eyes They're led Mystic Constant and M C square is the risk Most energy of the barnacle and our logistic momentum The equals Gummer times m u Here use the lost of the particle relative to an observer and their lead mystic factor Got my whiskey one by one, divided by the square root off one minus um, you divided by See Hold square And therefore let mystic momentum be equals. Uh, m times you divided by a squared Rudolph one minus you divided by sea whole script. Uh, let us consider an electron him speed, uh, having speed a 0.999 times the speed of light. All right, here, uh, C is the speed of light, and, uh, the rest must energy. Often, electron is given by most of electron times C square and most of electron time. C square is 0.511 million electron volts and ah, 0.511 million electron walls, um, can be rich in east end to the power six electron walls. And, uh, we have, uh, um uh, In jewels. It's equal to 0.8176 a 0.8176 Multiply by 10 to the power minus 13. Jules. Oh, are we can ride. This is 8.176 Multiply by 10 to the dollar, minus 13. Uh, Kimble crown meter, square or second square. All right. Now let's calculate a relentless tick factor. Gamma and gamma equals one divided by screen Rudolph one minus, uh, 0.999 times. See, divided by sea, whole square. And this gives us 22.4. And the total energy of the electron is gonna times M c square. We have a gamma, which is 22.4 multiplied by, um, M C Square is 0.8176 multiplied by 10 to the dollar, minus 13 and then for total, um, energy off the electron is equal to 18.3. Multiply by 10 to the power minus 13. Jules. All right, on DDE here. Uh, um, the ladies step momentum off the electron. Uh, B equals gamma times. Sometimes you and here gamma is 22.4. Multiply by massive electron is 9.11 multiplied, attended four minus 31 multiply by. Uh um, the speed of light and speed of light is three points. It'll zero multiplied by 10 to the power eat meter per second, and this gives us 6.1 to multiply by 10 to the power minus 21 kilogram leader for a second. But as we know they revel in the electron is given by land is equal to each divided by B on DDE. Therefore, land A H is 6.626 multiplied by 10 to the power minus 34 and divided by Welby is 6.12 multiplied by 10 to the power minus 21 and dividing the two numbers, we get 1.8 multiplied by 10 to the power minus for geen meters. Now we know that the energy reverent relation for foot on is given by equals. H C, divided by Lambda and lender equals XY, divided by E and putting the values um, 86.626 multiplied by 10 to the power minus 34 multiplied by three multiply magenta devour 80 speed off light divided by energy, which is 18.3, multiply by 10 to the power minus 13 and therefore Lambda equals 1.8 multiplied by 10 to the power minus 13 meters, which is the same is calculated. Ah, for electron. Well, the daughter, lad, Mystic energy of the electron is large compared to its ah rest um energy. So ah, Web lint off fort on eyes equal to revel in it off electron on bow tie 1.8 Multiply by 10 to the dollar minus 13 meters.

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