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An electron has a de Broglie wavelength of 75 nm.(a) Calculate its momentum.(b) Find its speed.(c) What amount of voltage (in eV) is required to acceleratefrom rest...

Question

An electron has a de Broglie wavelength of 75 nm.(a) Calculate its momentum.(b) Find its speed.(c) What amount of voltage (in eV) is required to acceleratefrom rest to the speed found in part (b)? [Hint: Think conservationof energy]

An electron has a de Broglie wavelength of 75 nm. (a) Calculate its momentum. (b) Find its speed. (c) What amount of voltage (in eV) is required to accelerate from rest to the speed found in part (b)? [Hint: Think conservation of energy]



Answers

(II) An electron has a de Broglie wavelength $\lambda = 4.5 \times 10^{-10}$ m.($a$) What is its momentum? ($b$) What is its speed? ($c$) What voltage was needed to accelerate it from rest to this speed?

Here. We have been given the kinetic energy of electron and we have to find the momentum speed and very violent. So Kinetic energy is half MV square and it is equal to 120 electron volts half M. S. Mosque. Mhm. Yeah. Mhm. Vehicle speed which is unknown and it is equal to 120 electron world. So we convert it into a jewel by multiplying it by 1.6 into 10 to the power -19. So this gives us equal to the speed of electron 6.49 into 10 to the power six m/s. So momentum B will be equal to mass times. Speed, Moscow 9.11 into 10 to the power -31 kilogram. And speed is 6.49 into 10 to the power six meter per second. So this gives us momentum equal to 5.91 into 10 to the power -24 kg meter per second. For part B. We need speed, which we have already found in part A. So speed v is simply 6.49 and two 10 to the power six meter per second. For part C. We newt equivalent we have limited given by lambda call to Japan to be. It is plans constant. Mhm. Mhm. And P. S momentum. Mhm. Mhm. Mhm. Mhm. Yeah. This gives us the identical to 1.12 into tend to the power minus 10 m. Yeah, to convert it into nanometers, we divided by 10 to the power -9 because one nanometer is 10 to the power minus nine nanometers. And this gives us 0.112 nanometers. So we have found the prevalence in both meters and nanometers. This completes the solution. Thank you.

For the first part off the question, we can simply use the liberal blessing, which relates the momentum on the Waveland. The question states that momentum be because toe age buy lamp on. If we just plug in Valence for age and Lambda Weekend, that mo mentum is 1.1 into 10 to the power. I'm just waiting for on sodas for the first part for the second part before doing, and we should make an assumption that the speed off the particle is nor militaristic on, we can prove that as actually scared after we complete the question. So we rearranged equation for the Barkley. And since Pete is more militaristic, we can write momentum or p equals toe end be then we can be arranging for V, which equals to age. Bye, Lambda. And if we just plug in the values for age and I'm Linda, we get that the speed is one point toe and two and the power six meter per second, and then we can prove that our assumption is an appropriate and alleged assumption by simply taking the ratio toe our velocity over the speed of light, which comes off as a really Raj really small number, which is for 50 for into 10 to the power minus three. Which proves that the spirits known related mystic and on our assumption it's Kurt. For the third part, we can use the Classical Canada Energy question on rights, which is half m b square on. We can simply replace V with our ratio, which is be by sea on just really against the former law, according to the rest of eternity. Speed off their issue. And if we just plug in the values we get that vanity energy is 4.17 electron balls.

Discussion back you button electron with 80 Brooke the reef length off five times. Stand part minus 10. It us to find the momentum my momentary associated with the police were flying for a hitch over Lunda. So the HST thanks constant, by the way thing. And we will get the momentum. Just about 1.3 sent for ministry for to find a speed. The U. S. T momentum that was phone right p closed toe, sometimes fee. So do you ve lost e just 60 went on develop I d mess electron and we should get notes. Well, Fife Stempel six. Just a second. And this is about 10 to po minus two. Orders off. Many tube smaller than see And so we have seen it to be known Relativistic. And we can use the non relativistic version off the Canty energy. Just have every square to recreate that to the voltage needle to accelerate the election. Which is she taking the charge of the electron multiplied by d potential difference or the voltage. So the actual voltage that is required take off and the square defined by the church electron I should get rotation of about six votes

So in this problem. So suppose we have a light whose wavelengths is 2.5 Michael meters. It's in part a lambda is 2.5 micrometers. And we can figure out too. The moment, um, off this photo. Soap equal h over lambda. So this gives us 2.65 times 10 to the negative. 28th kilograms. Made up a second. Okay. And in part B. So suppose we have the same momentum for the electron we gotta figure out. Will also diabetic off that electron soap. Equal envy. Right. So this p here is, uh, the body we found over here and am is the massive electro. I am equal 9.1 times 10 to the negative. Negative. 31 kilograms. So we're going to see that the velocity is, uh, uh to 91 Made of a second, and in part, see, So, uh, if if you want to compare the kind of energy of the lecturer in this photo So for this photo, the kind of energy has expression, P times seep. Right. So this video is ah, seven point 96 times tend to the native twenties jos and the for the electron, the kind, the kind that energy has expression half and the squid M is the mass of the electron and V is the one we found previously, which is to 91 made up a second. So this year gives us 3.85 times tend to the native 26 chills. So compare with the continental energy of the photo. We see that E p is actually ah, it is approximately able to tend to the six e r. A. So the photo kind of kinetic energy is much larger than the electoral kind of energy.


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