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[-/1.66 Points]DETAILSMY NOTESUse the equation for the energy of the electron In the Bohr model of the atom and the fact that hxR 2.180e-18 to calculate the energy ...

Question

[-/1.66 Points]DETAILSMY NOTESUse the equation for the energy of the electron In the Bohr model of the atom and the fact that hxR 2.180e-18 to calculate the energy of an electron in the given level of each of the following ions This Is equation 2.5 in the paper textbook and can be found by browsing the Fbook- Use notation with two decimal places. For example, 2.34e-22_ Hint: Each of the ions has different number of protons but all have one electronLevel (n)IonEnergy inLi2+

[-/1.66 Points] DETAILS MY NOTES Use the equation for the energy of the electron In the Bohr model of the atom and the fact that hxR 2.180e-18 to calculate the energy of an electron in the given level of each of the following ions This Is equation 2.5 in the paper textbook and can be found by browsing the Fbook- Use notation with two decimal places. For example, 2.34e-22_ Hint: Each of the ions has different number of protons but all have one electron Level (n) Ion Energy in Li2+



Answers

The Bohr model of the hydrogen atom states that the single electron can exist only in certain allowed orbits around the proton. The radius of each Bohr orbit is $r=$ $n^{2}(0.0529 \mathrm{~nm})$ where $n=1,2,8, \ldots \ldots$ Calculate the electric potential energy of a hydrogen atom when the electron is in the (a) first allowed orbit, $n=1$; (b) second allowed orbit, $n=2$; and (c) when the electron has escaped from the atom $(r=\infty)$. Express your answers in electron volts.

So using the Bohr model of the hydrogen atom, Um, which is the incorrect model, but it's an easy approximation. Theologian Tron orbits the proton, right? So since there's a hydrogen atom that it's a hydrogen atom has only one proton and one electron, and that has a radius of 0.53 times 10 to the minus 10 meters. The charge here that we're gonna use is the charge Q of equal. 1.6 times 10 to minus 19. Cool. Oh, that's the charge of a proton, Uh, and minus That would be the charge of an electron here. Okay, so for part a okay were asked to calculate the electric potential at the electrons orbit due to the proton. So the potential V is going to be equal to the constant K, which is one over four pi upsilon not equal to 8.99 times 10 to the nine Newton time meter squared per Coolum squared. It's a common constant. You can look up times the charge Q divided by the distance are plugging those values into this expression. We find that the potential is 27 bolts weaken box. Aydin is their solution for part a. Okay for part B. The kinetic energy here can be found from the fact that the magnitude of the net force on the electron, which is an attraction by the proton, is cause eyes causing the circular motion. So therefore, the kinetic energy K E is equal to 1/2 n v squared right, which is going to be equal to Ah, 1/2 okay, times the charge Q times The magnitude of the charge of the electron, which is minus Q, divided by the distance between squared. So where do we get that from? Well, we got that from the fact that the mass times that, uh, speed squared divided by our is the force. Hey, which the force here, of course, using Coombs laws Kay Q times minus Q. The magnitude of minus Q. Divided by are square so open actually had a type of this would be over our right. So then just playing in N v squared for uh, R R k e value, we find that in the squared is equal to K Q times minus the magnitude of minus Q over our. So that's where we got that now, plugging those values that we have into this expression, we find that this is equal to 2.2 times 10 to the minus 18. The units there would be Jules, you can then convert from Jules to electron volts. Son, this is equal to 14 electron volts. You can box the senate. Your solution for part B cancer, not cross out that 18 there. Okay, now moving on to part. See, So the total energy then here for part C of the electron is gonna be the sum of the kinetic energy and potential energy. You can use the equation 17 dash to A to find a potential energy. And it's negative, since the electron here has negative charge. So the total energy is going to be equal to the potential energy plus the kinetic energy. Oh, okay. Well, we, uh we just found the kinetic energy in the previous question, and the potential energy is going to be minus the charge Q times. The potential V. Okay, then plus the kinetic energy, we've found the potential V in part a. So plugging all those values into this expression, we find this is equal to negative 2.2 times 10 to the minus 18 Jules. Okay, well, this is just negative. The answer that we got in part B, right? This is just negative. 14 electron volts. Linkenbach said it is our solution to part. See? Okay. Now for part D. So if the electron is taken to infinity at rest, then both its potential energy and its kinetic energy would be zero. Right? Um, at infinity, there's no potential energy. And if its kinetic energy is zero right, the amount of energy needed by the electron to have a total energy of zero is just the opposite to answer of part. See, So it would be minus. Hey, you can Box said it is the solution for D.

Share Using the board formula for the energy levels, we have to calculate the energy required to raise the electron in a hydrogen attempt from N is equal to one to N is infinitely and we have to express the result for one more hydrogen atoms. And it is stated since in is infinity. Where it is promoted in equals infinity level corresponds to removal of electrons from the atoms. So this energy will be considered as ionization energy of the hydrogen atom. Now we'll use the ball formula. Delta E negative are raised. This is the constant juan in a square minus and initially a square so minus R. A. Is constant here, one by infinity Square and one x 1 square. So it will be negative. Our eight tons negative one. So it will be equal to delta A. Is equal to R eight. The constant and the value for this one is 2.17, 9 times 10 to the bar negative 18 june part hydrogen atoms. Now this energy equals the iron addition energy of the hydrogen atom. Why? Because in is infinity. This level corresponds to the removal of electrons from the atoms. So Iron Digestion, NFG for one more hydrogen atom is 2.179 times 10 to the power negative 18 jewels Bar one hydrogen atom times avocados. Number 6.2 times 10 to the part 23. 8 atom's far more hydrogen atom. So okay, The value is 1.31, 2 times 10 to the par six tool. Far more. Hi dujail and dumps That is 1.312 times 10 to the part three kilo june. When we divide by thousands, kill a juice bar more hydrogen atoms. So the iron addition energy for one mole of hydrogen atom is 1.312 times 10 to the power three kg jew.

Hello, friends. Here it is. Given the voter model off, hydrogen atoms escapes that single electron can access only in certain allowed or which around the proton, the Raiders off each word orbit is our school toe Any square in tow? Why, you know, 5 to 9 nanometers here and maybe 123 This is called quantum number. We have to calculate electrostatic potential energy. You We have to calculate what first in the first orbit that is for and it's called to burn second for and it's goingto see has escaped from that tumble are it's cult unitary from Adam at our school Doing pretty we have to express the result in electric book Let us see it first part electrostatic potential energies He Cuban queue to buy our He is nine in 10 toe the overnight charge on the protons charge on revolving electron for first orbit, and it's called to burn one guy square in tow. 2005 tonight and tow 10 to the power minus 9 m on solving it, it would be minus four point. Do you fight and tow 10 to the power minus 18 you are. It will be 27 points. Just a moment I'm writing. He has a huge culture. You will get minus 27 points. Electron world. Yeah, No be point in. The second orbit formula is nothing. He is 9 to 10 to the governor. Nine Cuban charge on proton in the nucleus. Charge off. Electron revolving around it in second orbit. That is to square. So it would be 1/4 off 27.2. So directly we can write minus 6.8. Do your will upon bolt, See, at a predict. Okay. You want you do by infinity. So it will be zero. That's all for it. Thanks for watching it.

In this problem, daughter energy off a particular book. Her orbit is given and you want to calculate kinetic energy and potential energy. Abda his tongue. So here we have the energy of the war. Are is a little bite minus little bart and for life and it blown world. In the first part we want to calculate kinetic an idea of the stone. And in the second part, we want to call coolant partition. And now you have the system s we hell the relation for totally now gene war are bit is he's a Kal toh minus gear. He's a girl. A bomb Are here case columns Constant. He's Judge Onil Adan Are Is war orbit ready? Yes. And we also hear the relation for kinetic energy off when they're done in war are rich use. Okay. You call too. Yeah, he's good. A bomb. Oh, so this is kinetic energy s kinetic energy are kinetic Energy and trip energy are equal in magnitude So we can write, you know, technology off don as kinetic energy easy gold toe minus daughter energy. So by putting the way you are forgetting that here we have kinetic energy. Is it Kal Toh minus. He had one of these minus your point and five at a turn world. So we help kinetic energy of the system Equal toe Dana Point and five electron word. There's dust it off. But a of this problem live in the second part. We want to calculate for originality of the system as we help the relation for total energy. There are energies you, Kal Toh, some off gonna dignity and potential energy. So from here, we hope for right hander Jeezy Kal Toh daughter Energy minus Ginna Dick Energy as hell. Total allergy is minus you know point and five and a turn world and a kinetic energies Zero point and five turn world. So we help. We're praying that the other system equals two minus one. Fired seven. I looked down on work their sensor. Thanks for watching


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