Problem

Integrated Concepts (a) What is $\gamma$ for a p…

Problem 77 Hard Difficulty

Integrated Concepts
(a) What is $\gamma$ for an electron emerging from the Stanford Linear Accelerator with a total energy of 50.0 Gev? (b) Find its momentum. (c) What is the electron's wavelength?

Answer

a) $6.23 \times 10^{-7} \mathrm{J}$
b) $2.67 \times 10^{-17} \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}$
c) $2.48 \times 10^{-17} \mathrm{m}$

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Physics 103

College Physics for AP® Courses

Chapter 29

Introduction to Quantum Physics

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Video Transcript

this problem is asking us to solve for our Larenz factor, also known as gamma, if we have an energy of 50 giga electron volts So our energy is equal to our Larenz factor times mass times the speed of light squared So energy divided by mass times The speed of light squared gives us our Lauren's factor and our energy is in 50 Giga Electron volts. But it is helpful to have that number in mega Lo jungles, so we can actually convert it. And that would be five times 10 to the fourth mega allergic. This problem is asking us to soften our Larenz factor, also known as gamma. If we have an energy of volts, we can use that number here and our mess of our electron if you look at your charts, can be written as 0.5 11 mega electron volts per speed of light squared. And that number is just helpful because when we multiply this value by the speed of light squared than this 50 giga electron volts. So our energy is equal to our Larenz factor times mass times the speed of light squared so energy divided by mass times the speed of light squared gives us our Lauren's factor, and our energy is in 50 Giga Electron volts. But it is helpful to have that number in Mega Lo and jungles, so we can actually convert it. And that would be five times 10 to the fourth mega trump Speed of Lights counsel. And we don't actually have to use them in our equation and our mega electron volts also council, which gets me a value of 9.7 eight if you round times 10 to the fourth. And again, this is aren't Lawrence Factor Apartment. The part B were asked to calculate the mo mentum. So again, momentum is art will runs factor in this case, Tim's mass times velocity. Because we're talking about the electron, the speed is going to be, um, these cables we can use that number here and our mess of our electron. If you look at your charts, can be written as 0.5 11 mega electron volts per speed of light squared. And that number is just helpful because when we multiply this value by the speed of light squared than those of lights, so our Lawrence factor is 9.78 that we just calculated times 10 to the fourth. Our mass can just be are 9.11 our usual mass for an electron times 10 to the negative 31 kilograms and our speed of light can be ratcheted three times 10 to the eighth meters per second Which gets you a Momenta MME of 2.67 times 10 to the negative feet of lights Counsel. And we don't actually have to use them in our equation. And our mega electron volts also council, which gets me a value of 9.7 eight if you round times 10 to the fourth. And again, this is aren't Lawrence Factor apartment The part B were asked to calculate the mo mentum. So again, momentum is art. Well, runs factor in this case terms mass times velocity because we're talking about the electron, the speed is going to be, um, the speed 17 kilograms meters per second. And then for part C, it is asking for you to solve for your ah weakling. So our wavelength can be calculated by our planks constant invited by our momentum that we just solved for so our planks cause is it that we're using a 6.63 times, 10 to the negative, 34 jewels, time, seconds of lights. So our Lawrence factor is 9.78 that we just calculated times 10 to the fourth. Our mass can just be are 9.11 our usual mass for an electron times 10 to the negative 31 kilograms. And our speed of light can be ratcheted three times 10 to the eighth meters per second which gets you a Momenta MME of 2.67 times 10 to the negatives are mo mentum That we calculated was 2.67 again. You should be using the entire number that you have in your calculator times 10 to the negative 17. You can't kilograms meters per second and this gives us a wavelength of 2.48 times 10 to the negative 17 meters.

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