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NamecollaboratorsPhysics 118 Quiz 5-2In the Bohr model of the hydrogen atom; we found E= -13. ev; K= 13.6 eV; Uz -27.2 eV, and 0.0529 nm:Calculate the de Broglie wa...

Question

NamecollaboratorsPhysics 118 Quiz 5-2In the Bohr model of the hydrogen atom; we found E= -13. ev; K= 13.6 eV; Uz -27.2 eV, and 0.0529 nm:Calculate the de Broglie wavelength of the lectron its orbit b) Calculate the de Broglie frequency of the lectroncompare to the circumference ofcomparethe orbital frequency:

name collaborators Physics 118 Quiz 5-2 In the Bohr model of the hydrogen atom; we found E= -13. ev; K= 13.6 eV; Uz -27.2 eV, and 0.0529 nm: Calculate the de Broglie wavelength of the lectron its orbit b) Calculate the de Broglie frequency of the lectron compare to the circumference of compare the orbital frequency:



Answers

a. Calculate the de Broglie wavelength of the electron in the $n=1,2,$ and 3 states of the hydrogen atom. Use the information in Table $29.2 .$ b. Show numerically that the circumference of the orbit for each of these stationary states is exactly equal to $n$ de Broglie wavelengths. c. Sketch the de Broglie standing wave for the $n=3$ orbit.

In this question. Do you want to co create What is the boobies? Riffling for the electrons is different states by using the table 39.2 So from 39.2 we can find you think so? I didn t blow grease Rethink is equals to hate you for a fee, right? And from the table, we should get the velocity 40 different end states. So for any Costa one, the wavelength will be dependent on the velocity of the electron in the any coast one states. So we could just stuff to do that which is given s 2.1 night person poll six Just a second And we should get our we think to be is your point tree too, You know, we do the same thing. Just substitute different values off velocity she get London to two p 0.665 Meet us and under a tree to p 0.997 centimeters. Not to proof that our circumference off the obvious IHS equals to our table key. Swiftly or multiple off are the bookies refit right? Be needs the radius off our orbit which is given S. R n just keep goes toe and square. I want to play by our HST boss radius i o a p for n equals two one The radius be just goes to R B, right, That's all one. Then there's the conference. Will be goes two pi r Thanks conferences two pi R one, which is two pi times. You appoint your 5 to 9 nanometers which we gets your point tree tree two centimeters, which is exactly equal to our Atlanta one. Same thing. We're gonna do, uh, find the radius Often it's a conference for ah sickened orbit, that is two pi times are too. We should get one point tree tree too in a retest just because toe to times off your 0.665 millimeters thanks So that it goes to two times off to finally see tree, which is two pi r tree. We would get the same relationship which is three times off under a tree. So what? This tells us, you said, uh for and a bit for the state and the orbit would have is a conference that can accommodate and number off with links off the ball reflex, right? Uh, and we want to troll the a bit shape or the D probably standing wave for any question tree. So that s every day. So go first. Now, any question tree instead, the circumference woods accommodate three times off the wavelength off our Debo Greece with things and what has insisted. Related feats in tree pass off peak and trough. Right. So this is one brief fling, peak and trough. So we need to have this three times over the entire orbits. Sortie, 62nd time and our time like so the Obi it should look something like that.

Solving party of this problem. So we all know that linda is equal to urge by mp. Which can be further written edge 6.63 multiplication 10 to the power minus 20 for jules. Again by 9.11 multiplication 10 to the power minus 31 kg, multiplication 2.19 multiplication 10 to the power six m purse. Again on simplification I gave the value of blame diet 0.33 Multiplication 10 to the power minus nine m On simplifying it further I get the answer at 0.33 and um and m as our answer now solving part B. So for part B I can write the circum parents of the orbit is equal to two pi R one. So just putting the value I can write to multiplication prime multiplication 0.5 to nine which is equal to 0.33 nm. So the plant we obtain is nearly the same as the circum parents of the first orbit.

Okay. And this question we're asked to find the Detroit the wavelength of the electron um that is orbiting around hydrogen atoms. So we have to do this for an equals one and an equal score. Ah So this is the formula for leaderboard, the wavelength. And we just need to find the velocities of the electrons at those Uh two different energy levels. Um So, if we can know the energy, um then we can connect energy to velocity. Using kinetic energy, So equals 1/2 and b squared. Um and then we'll solve for uh the the kinetic energy. So he is equal to the square root of two times kinetic energy provided by the mass of the electron. Uh So we need to find the kinetic energy um using the um orbital potential energy. Uh So, since the orbital potential is balanced out by the kinetic energy, we can use a burial theorem, which is that use equal to -2 times, Katie uh realize that kind of minus on it here. Um So Kay is going to be -1 half of you. Uh So that's going to give us um ah K. E two or Katie one and K. E four. Um from from this formula applied to these values. So we can plug those then into this formula, she's going to give us the velocity and then we can plug the velocity back into the devoid the formula. So when we do all that, what we get is that Lamda won the wavelength uh right away. Banks electronic. The first energy level is 4.702 times tanks To the -11 m. And lambda four. The boiler wavelength of the electron At the 4th energy level is 1.73, 5 times 10 to the 9th to the -9 m. So I found the deploy the wavelength and then in part B. Um What they ask us to do is compare the uh wavelengths to the um circumference of the that they travel around the um around the nucleus. So uh we're going to compare is lambda over girls, lambda and over two pi Marcel van. Uh This is just obviously the corner for the circumference. Um and our Saban is equal to and squared times are 60, our absolute to use bar radius. uh so we can just um plug in and equals one and equals four and then divide those values and Atlanta one over two pi R one, it's equal to 0.014. And and the 4/2 pi RC four is equal to zero 005 And we're done. Mhm.

In this question. We need to find electrons are with radios. Uh, they brought me, we're playing kind of speed for hydrogen atom. And uh, and it goes to its state. Okay. So find a hobby to radios he would be using and it goes to end square or not. So, and if you go to eight, so are it is 64, you know, you know, it's forages Because with 0.05-9 times 10 to the -9 with us. So you can live in um, you don't mean that as well, Then you can get 3.39 mm, you know, with us. Okay. Okay. So this is the answer. Uh, a okay papi want to complete the you brought me with me. Okay. So, um, yeah, given that the, the body were playing is actually equal to the um, circumference. Thanks the thanks to mm states the energy level the number so linda and it goes to end. Thanks to buy, you know, Okay. So I'm not eight is 8 times two pi times. Yeah. 0.0529 mm. Okay. So the replying is a trip country nine And 2.66 66 And yes they want to campaign uh the speed of the electron. So Using the Formula 40 properly rippling like divers to Asia repeat uh oh which is issued A. And B. So B. Is equal to each of em London. Okay. So you're subject to their numbers. The mass of the electron is 911 times 10 to the power negative one hee. Okay. And then Lunda is 2.66 times a negative nine does. Okay? You copy this? Other speed is 2.4 And 10 to the five. He does for a second. Yeah. And the party want to use balls theory to complete uh the orbital speed you would be using M. B N. R N. Goes through and each over two. Okay. And and is equal to eight. So be it is eight h by two pi and our IT he so that's playing the numbers. They are S. S. Treatment to end with this he and your goods I took myself for and send the qualifying with us for a second came to this is the same same as you can see, right? So which is expected? Great cannot be, this cannot be different. Okay. It is good. And then that's all for this question.


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