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Calculate the wavelength, in nanometers, of an electron movingat a speed of 1.60 x 10^6 m/s The mass of an electron is 9.11x 10 − 31 kg and Planck's con...

Question

Calculate the wavelength, in nanometers, of an electron movingat a speed of 1.60 x 10^6 m/s The mass of an electron is 9.11x 10 − 31 kg and Planck's constant is 6.626 ⋅ 10 − 34 kg xm2/s

Calculate the wavelength, in nanometers, of an electron moving at a speed of 1.60 x 10^6 m/s The mass of an electron is 9.11 x 10 − 31 kg and Planck's constant is 6.626 ⋅ 10 − 34 kg x m2/s



Answers

Calculate the wavelength of an electron moving with a velocity of $2.05 \times 10^{7} \mathrm{~m} \mathrm{~s}^{-1}$.

For a were asked to calculate the wavelength and kinetic energy of an electron beam that has been accelerated by voltage increments of 100 volts. Wavelength is equal to each over M B and the kinetic energy equal to one half m V squared, which is equal to the momentum squared over to em. Momentum is equal to mhm Thembi, which is equal to the root of two m. Okay, so the wave length is equal to H over mhm. The square root over to the mass of the electron kinetic energy of the electron and the kinetic energy of the electron is equal to 1.602 times 10 to the minus 19 times one electron volt mhm physical to 1.602 times 10 to the minus 19. So the wave length is equal to 6.626 times 10 to the negative. 34 over the screw root two times massive electron times 100 thoughts times one point 602 times 10 to the minus 19. And this is equal to a wavelength of 1.2265 times 10 to the minus 10 meters. Yeah, and then for energy here. The kinetic energy here is equal to, um Oh 1602 times 10 to the minus 19. Okay, times 10 to the two or 100 vaults. And this is 1.602 times 10 to the negative 17 jewels. Here's our wavelength. And here's their kinetic energy. For part b, calculate the kinetic energy of an electron that has a de Broglie wavelength of 200 people meters. So wave length is equal to place constant discouraged to em the And then we've got our kinetic energy here. Okay, mhm and rearranging. Kinetic energy is equal to each squared over to, um times The wave length squared 6.626 times 10 to the minus 34. This is two times the mass of the electron mhm times the wavelength 200 times 10 to the minus 12 people meters squared. And this would work out to a kinetic energy of 6.2 times 10 to the minus 18 jewels

Using two broke Li's wavelength formula. We can calculate the wavelength of light if we know the mass of it, our wavelength of a particle for you know, the mass of it and the velocity of it. So if we haven't Electron given that is traveling at 1.35 times, 10 to the 50 meters per second, we can figure out its way blank using this particular equation. So the wavelength would then be equal to Plank's constant, which we are going to list as six point 626 And rather than Jules, we're going to put the equivalent of a jewel, which is telegrams times meters over second squared times a second over mass of an electron and a mass of an electron is 9.11 times 10 to the negative, 31 kilograms times its velocity, which in this case was 1.35 times 10 to the fifth meters per second. So this one, the seconds gets crossed out there. The other one crosses off. Here, you have kilograms crossing off here, and when you go through and calculate this because this was meter squared, you're gonna end up with 5.39 Now, leaders was the wavelength

Okay. So for this one, we want to find the speed of an electron having a competent. It's comfortably blank, people to is to brutally with flying. So Compton wavelength is cool. T h over m c. So why let Liam to see Is each over m c? And I'm sorry, Is that one of his age? Yes, over embassy. And then we want to set it equal to the de Brookly way. Playing took probably wavelength, which is people t h o ver p. And then we want to use relativistic mo mentum. So I think you just end up putting a gamma in front of it. I'm gonna pause the video. Well, I look it up. No, you just put a game in front. So, um and then what's cama? Uh, Gammas. So we have m v. And then gamma is the square root of one who was at minus her. Plus, don't forget that one minus b squared over speaks part. I don't know of a great way to remember it, but I guess if I I do relativity, we'll probably find a nice way to remember it. Royalty Vitti chapter. Okay, so now we want to solve for this vys. That's gonna be kind of analogy. Break mess. Hopefully, it's not too bad. Let's start by canceling those. Let's get some stuff out of the denominator by cross multiplying. Oops. I should have canceled that sorry over here, so it didn't really make sense to cancel that. So and then Oh, actually, this is kind of nice. The masses also cancel. So, basically, now, let's go ahead and move Everything, um, elsewhere. So So I'm gonna bring the sea over here, so C is equal to V over the square root of one minus V squared over C squared. That's gonna interesting. Really Doesn't depend on in any physical constants. Um, double tracking The entrepreneur looks good to me. Now we need to solve for V. All right, so here's where the algebra mess comes so we can square. Both sides might try to take some shortcuts to avoid, like, tons of different lines. Well, that was seamless. Okay. And then let's multiply both sides by one minus. V squared over C squared. So bring this over here. Actually, this could be kind of fun. Thio, uh, try to do all the Al Jeroen online so I multiply both sides by that great and then oh yes, it's really not so bad. So let's distribute the C squared and I will do any line for that. C squared minus B squared equals b squared. I could bring the B square to the other side so adding plus V squared to both sides when it's that makes this to be square and then great. And now I end up with us such a simple result that V is equal to the square root, um of 1/2 just multiplied by C. That was fun. So I guess it has to be basically on part of the speed of light for the confidently like equal to its superbly with thanks.

Mhm. Let us calculate the deep appropriate violence of an electron moving at 20% 20%. The speed of life. Mm It was assumed electron moving around the circular RT. According to the deal bro grill. The baby went lander equal to hatch divided bike. Um We hear rumblings the Waveland And how much is it constant? So who's constant value is 6.266.626 Into the into the Power -34. Yeah. And um asia most of particle Holston. Also political is 9.100 Grammy. It's a constant battle. War and political 9.1 times Into the Power of -31. Yeah. Yeah. Hear hear the election moving at 20% of the constant speed of life. Thus we know the constant speed up like this please. 28 to 8 times 10 to the power of eight m pulse a hand. So We just want to find the velocity for 20%. Constant value of velocity of 20%. Which would be I want to give it a month. 100. Sorry, don't you do anything 100 times. Yeah. Three point age. Come on. Uh huh. No problem. You deposit him. So make my day you can do the follow up. Mhm uhh Meet oppose it. What about Some people like this? We get seven points. So 76 and you go into the power since 20 times that we might take this emphasis and then we have been to the correct way and here that is to you know, interesting. So 10 to the power of the ministry. To the power of two or 3 weeks. 10 to the power of six. So we have that Velocity we equal to 76 times came to the border of six. Let us have played the normal value in the form a lot. So I'm not the baby land. We get lambda is supported six points exclusives Into into 10 to the power of minus the people. Yeah. And the communities program. Make this clear. Second english. Do you want to buy Most of Most of the Particle? 21? Okay. And you came to the power of -30 31. Mhm -31. You just kill over. So the most of the particle uniquely kilograms. Yeah. In two we found the velocity scientists explains Into the power of six m second english. Meet the goals. Come on you got it. So it does simplify the denominator post. Thank you. We get 9.1 times 76 is here we have with Into the part of 31 and into the problems things. So when simplify this dance we can get six point 916 and took into the Barbara minus 23. And uh and the numerator is six, explosion entered into the cover of minus 34. Okay, right. The unit is the telegram and the american telegram. Get cancer. 2nd ingles also cancer and meat as well. We have one elite 1 m in the refrigerator. So simplify these towns. And so do I. These students. We catch £9 x 81 input into the cover up minus to a meter. So it is the um, it is the violence of the electoral electron moving a 20% speed of light.


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